ANSWER ONLY NUMBER 5 Show all necessary solutions.1. A random variable X denotes the number of books bought by a customer in a bookstore. Weknow that the random variable has the distributionP(0 < X< 1) = E P(1 4).%3D12Compute P(X = i) for every i = 1, 2, 3.2. Let F be given byif t < 0,aif t € [0, 2),2c +b if t e [2, 3),F(t) =dif t > 3.a. Under which conditions on a, b, c, d is the function F a cumulative distribution function?b. Assume that F is the c.d.f. of an r.v. X. Compute the law of X.3. Let X ~Geometric(p) with pe (0, 1). Prove that for every a, b eN we haveP(X = a + b|X > a) = P(X = b).4. Let X be a discrete random variable with the following distribution:P(X = -3) = a, P(X = -2) = , P(X = -1) = b,P(X = 0) = 6, P(X =1) = c,P(X = 2) = 2a. Find a, b, c.b. Calculate E(3+ 2X), E(3+ 2X), Var(3+ 2X).5. Derive the expected value of the random variable X with distribution Negative Binomial(r, p).

Name: ANSWER ONLY NUMBER 5 Show all necessary solutions.1. A random variable
Uploaded: 2024-03-20T07:06:41.000Z
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Description: ANSWER ONLY NUMBER 5 Show all necessary solutions.1. A random variable X denotes the number of books bought by a customer in a bookstore. Weknow that the random variable has the distributionP(0 < X< 1) = E P(1 4).%3D12Compute P(X = i) for every i =