f(x) = ²(2-x) for-1 ≤ x ≤ cand f(x) = 0 otherwise.(a) Explaining your work, find the value of the constant c.(b) What is P(X > 1)?(c) Calculate the expectation of X.(d) Calculate the variance of X.C2. For each of the following, (a) calculate the exact value using R; (b) get an approximate value usingan appropriate approximation and without using R. (Statistical tables are available.)(i) P(X ≤ 3), where X~ Bin(1000, 0.005).(ii) P(296 ≤ Y ≤ 307), where Y Bin(1200, 0.25).(iii) P(Z ≥ 398), where Z~ Bin(400, 0.995).

"Since you have asked multiple questions, we will solve the first question for you. If you want any…

ƒ(x) = ² (2 − x) for -1 ≤x≤c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.

ƒ(x) = ² (2 − x) for -1 ≤x≤c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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Question

f(x) = ²(2-x) for-1 ≤ x ≤ c
and f(x) = 0 otherwise.
(a) Explaining your work, find the value of the constant c.
(b) What is P(X > 1)?
(c) Calculate the expectation of X.
(d) Calculate the variance of X.
C2. For each of the following, (a) calculate the exact value using R; (b) get an approximate value using
an appropriate approximation and without using R. (Statistical tables are available.)
(i) P(X ≤ 3), where X~ Bin(1000, 0.005).
(ii) P(296 ≤ Y ≤ 307), where Y Bin(1200, 0.25).
(iii) P(Z ≥ 398), where Z~ Bin(400, 0.995).

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