2. The probability density function of a random variable X on [2,5] is given by 1 f (x) = 1- Vx - 1 Find P (3 s X s 5).
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![2. The probability density function of a random variable X on [2,5] is given by
f (x) = 1-
Vx - 1
Find P (3 s X s 5).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c2bc640-b23d-4ce6-a622-ddf16412bede%2F51b8a19e-b239-41ca-b5f1-5e8599a334e6%2F4gcxcpt_processed.jpeg&w=3840&q=75)
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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)=___________.Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?
- Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.Suppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?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 otherwise
- 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 2Q3) The joint probability density function of two discrete random variables X and ¥ is given by p(x, y)=c(2x+3y), where x and can assume all integers such that 0 <Suppose the joint probability density of X and Y is fX,Y (x, y) = 3y 2 with 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 and zero everywhere else. 1. Compute E[X|Y = y]. 2. Compute E[X3 + X|X < .5]