Show that for any random variable E[X2]≥ (E[X])² and When does one have equality?

Q: For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))

A: Given, Two random variables X and Y such that X~Exp(0.5) and Y|X=x ~N(5,x2)

Q: Find fQ|X (q|x) for x ∈ {0, 1} and all q.

A: It is a fact of statistics. It is widely used.

Q: For a certain random variable X it is known that E[X]=2, Var(X)=3. What E[x']?

A:

Q: Let X₁, X₂,..., Xn be a random sample from an exponential distribution with the pdf f(x; 3) = ¹e/³,…

A:

Q: Suppose X is a continuous random variable with p.d.f. fX(x) = kx2(1 − x) if 0 < x < 1. (b) Find the…

A:

Q: Let X be a positive random variable; i.e P(X ≤ 0) = 0. Which one is correct? (1) E (+) (²) (11)…

A: Given:X is a positive random variable, meaning .We need to determine which of the statements is…

Q: If X is a uniform random variable over the interval (8, 12), find E[X]

A:

Q: Let X be an exponential random variable with standard deviation σ. Find P(|X − E(X)| > kσ ) for k =…

A: Let X be the random variable distributed exponentially with parameter λ.   Since the standard…

Q: Suppose that X is a random variable for which E(X) = μ and Var(X) = σ2. Show that E[X(X − 1)] = μ(μ…

A:

Q: Let X be a continuous random variable with pdf f(x) = x² for -1 < x < c. Find the value of c.

A: From the given information, the pdf of the random variable X is,

Q: A number X is randomly selected from the interval [10, 15]. The PDF of X is 1 15 - 10 0 1. Find the…

A: The pdf of a random variable X is given by: fXx=115-10    if x∈10, 15      0           Otherwise=15…