Let X will be continuous random variable with probability density function as below. (4x3 0 , otherwise (0
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.
- If X is a continuous random variable with probability density function f(x)={x, if 0<x≤√2,otherwise x=0. then E(X)= (provide an exact answer) and Var(X)= (provide an exact answer).Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)
- Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.Let X be a random variable with probability density function f(x) = x/8, where x = 1, 2 and 5; 0, otherwise. Find the expected value of x.
- Determine E(X), E(X2) and V(X) if X be a continuous random variable with probability density function fx(x) = 3x^2 0 ≤ x ≤ 1 0 otherwiseSuppose that X is a continuous random variable with density function f(x). If f(x)=k for −5≤x≤3 and f(x)=0 otherwise, determine the value of k.If the probability density function of a continuous random variable X is f(x) =⎧ kx2 0 ≤ x ≤ 2⎨⎩ 0 otherwise then k is what? A. 2B. .25C. .375D. any positive value greater than 2