Given that a random variable X have a Poisson distribution with 2; Find E[cos(nX)] if E(X) = In 2

Q: Consider a random variable X that follows a Beta distribution with E[X] : Find the method of a+1"

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Q: Given that X is a continuous random variable that has a uniform probability distribution, and 0…

A: A random variable X~U(0,1)f(x)=1 ; 0<x<1

Q: The random variable X has a Poisson distribution and is such that P(X)= 2 = 3P(X= 4). Find these,…

A: Assuming P(X=2)=3P(X=4) x~Poi(x),λ>0P[x=x]=e−λλxx!P[x=2]=e−λλ22!P[x=4]=e−λλ44!∴ Assuming…

Q: Suppose that X and Y have the following joint probability function: 3r, if0<y< a<1 0, f(x, y) =…

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Q: Let X be a Poisson random variable with E[X] = ln2. Calculate E[cosπX]

A: Given: Let X be a Poisson random variable with E[X] = ln2. The objective is to calculate E[cosπX].

Q: The weight of a hot-rolled steel beam is to be modeled as a lognormal random variable with a mean…

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Q: 1. Given a random sample X, from a population with density f(x; 8), show that maximizing the…

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Q: If X,, X2,...,X, constitute a random sample of size n from a population with p.d.f. given by .....…

A: Find MLE of θ

Q: The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X= 2).

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Q: 1. Let X be a Poisson random variable with parameter A. Derive E(X) and E(2x)

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Q: Suppose X has a Poisson distribution with parameter A and suppose the conditional distribution of Y…

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Q: The PDF of random variable x is given as, 0.3507 Jx, 0<x<3 1,(x): 0, otherwise Find the, Mean

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Q: An atom in the ground state of a quantum harmonic oscillator has a wavefunction ψ(x) that gives rise…

A: From the given information, ψx=14*2π14e-x2-4x+41024ψx2=142π14e-x2-4x+410242…

Q: Given that the discrete random variables X has probability mass function, Pr(X=x)= (x/6 where…

A: The probability distribution table is  x p(X) cf 1 0.166667 0.166667 2 0.333333 0.5 3 0.50…

Q: Let X1,..., X,|A be iid Poisson(A), and let A ~ Gamma(a, B), with a, B are known. Give two reasons…

A: Given information: The probability density function of the random variable X is as given below:

Q: Given that a random variable X have a Poisson distribution with 2; Find E[cos(nX)] if E (X) = In 2…

A: Given information: X is a random variable following a Poisson distribution with λ. EX=ln 2 It is…

Q: The cumulative distribution function for a random variable X is given by: 1-e for x20 F(x)=-…

A: Given the cumulative distribution function for a random variable X as FX=1-e-2x           for   x⩾00…

Q: The random variable X has a Poisson distribution such that P(X=0)=P(X=1).  Calculate P(X= 2).

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Q: Suppose again that Y is a normally distributed random variable with mu = 10 and sigma = 2. The…

A: Given Data Population Mean,μ = 10.0 Population Standard Deviation,σ = 2.0

Q: Given that the discrete random variable X has probability mass function, Pr (X = x) = x/6 where x =…

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Q: A random variable, x, has p.d.f. f (x) given by f(x) = 2 when 0< x < 1, The expected value is…

A: Solution

Q: If the joint cumulative distribution function of random variables X and Y is F(x,y) = (1– e-*)(1-…

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Q: If X is Poisson random variable with parameter λ, compute E[1/(X + 1)]

A: We have given that If X is Poisson random variable with parameter λ,  we have to compute E[1/(X +…

Q: Consider a random sample X1, . .. , Xn with n > 3 from the exponential distribution with parameter >…

A: A continuous random variable X is said to have an Exponential  λ distribution and has probability…

Q: Suppose N is a Poisson random variable with mean A. Show that E (1+ for any constant a. +a)^

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: Suppose that independent observations a1, r2,...,n are available from the log-normal distribution…

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Q: p.d.f. h(x) of the random variable x is defined by h(x) =3/(4(1-x²)),-1<x< 1,Calculate the standard…

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Q: The CDF of a continuous random variable X is F(x) = 1 - e-/5. Then the pdf of X is

A: We have given that, CDF F(x) = 1 -e-x/5 The pdf is given as f(x)= d/dx( F(x))

Q: If øx(@) is a characteristic function of a random variable X, then , (co) = 6, (@), where c is a…

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Q: 4. For a Poisson distribution X~P(A) (A > 0), which one of the following values does equal to? A. 1…

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Q: Let X be a beta distributed random variable having parameters a = 3.27 and 3 = 4.95. Find E[X²®(1 –…

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Q: Let X1, X2,..., Xn be independent exponential random variables with mean if. For example, E(X1)=0,…

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Q: If X1, X2, X, is a random sample from an exponential population having mean 1 find the exact…

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Q: If the discrete random variable X has the pmf for 2-1,0,1,3, a = find E(X), and var(X).

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: A random process X(t) is defined as X(1) = A.cos(27 fd)+A, sin(27fd) where A, and A, are independent…

A: From the given information, X(t)=Accos(2πfct)+Assin(2πfct) And E(Ac)=0V(Ac)=σc2E(As)=0V(As)=σs2and…

Q: e. For a random sample of size 3, obtain the probability that the sampling error made in estimating…

A: According to the central limit theorem, x¯ will follow a normal distribution with mean equal to the…

Q: 0, x)

A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…

Q: Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).

A: When X~ Pois(λ) P(X=x)=e-λ λx/x!  ; X=0,1,2,3,.. result: r!=r(r-1)(r-2)..3x2x1

Q: 2" Find the characteristic function of the Erlang distribution given byf(x) = n - -ax e U(x) and…

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Q: A random variable X has the following pdf: f(x) = 9xe-3";x > (a) Calculate the expected value of the…

A: Let X be a continuous random variable taking values in interval -∞,∞ with probability density…

Q: Suppose X is a random variable with following pdf: f(x)= pe-x+2(1-p)e-2x;  x>0          0,…

A: The probability distribution function is : f(x)=pe-x+2(1-p)e-2x,x&gt;0 The cumulative distribution…

Q: Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln√X] using Jensen’s…

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Q: Suppose a random variable X has a Bernoulli distribution for which the parameter O is unknown (0…

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Q: a) Suppose that X₁, X₂, X3.....X₁ is a random sample of n from population X which has a c square…

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Q: IfX is a random variable that has a uniform distribution on the interval [o, 10), then PX+ 10 27 is…

A: Continuous uniform distribution: A random variable X is said to have the rectangular distribution or…

Q: (a) Let Y be a random variable distributed as X. Determine E(VY) in terms of r.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Consider a random sample X1,..., Xn with n > 3 from the exponential distribution with parameter > 0…

A: Given that X1,......,Xn are random samples with n&gt;3 from the exponential distribution. The…

Q: Suppose X is a random variable whose pdf is given by f(x) =k(4x-2x^2) 01)

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Q: Given that X has the probability distribution f(x) for a 0,1, 2,3, and 4. 16 Find the…

A: Moment Generating Function (m.g.f.): Let X be a random variable with probability function…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!