Problem 4. Let X have density f(x) = cx²(1-x)² for 0≤ x ≤ 1, and f(x) = 0 elsewhere.(1) Find c.(2) Calculate E(X).(3) Calculate V(X).

1) c= 302) E(X) = 1/23) V(X) = 1/28 Explanation:

Answered: Problem 4. Let X have density f(x) =…

A First Course in Probability (10th Edition)

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Problem 4. Let X have density f(x) = cx²(1-x)² for 0≤ x ≤ 1, and f(x) = 0 elsewhere. (1) Find c. (2) Calculate E(X). (3) Calculate V(X).