6e-(2x+3y) fx.y(x,y) = x≥0, y ≥0, 0 otherwise.
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Random variables X and Y have joint
a) Find P[X > Y] and P[X + Y ≤ 1]
b) Find P[min(X,Y) ≥ 1]
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- #5Show the density func in table form and show complete solution.Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.
- Given: image Find the following: show sol. a) Conditional pdf of Y given X=x b) Conditional Expectation of Y given X=x c) Conditional variance of Y given X=x3. Let the random variable X have the pdf f(x) = 2(1 — x), 0 ≤ x ≤ 1, zero elsewhere. a) Find the cdf of X. Provide F(x) for all real numbers x (set up the appropriate cases). b) Find P(1/4 < X < 3/4). c) Find P(X= 3/4). d) Find P(X ≥ 3/4).Let X be a random variable on a closed and bounded interval [a, b]. Let g(x) be a convex function. Prove that g(E(X)) ≤ E (g(X)
- Let X be a point randomly selected from the unit interval [0, 1]. Consider the random variable Y = (1-X)-¹/2 (a) Sketch Y as a function of X. (b) Find and plot the cdf of Y. (c) Derive the pdf of Y. (d) Compute the following probabilities: P(Y > 1), P(3 < Y < 6), P(Y ≤ 10).A1 Please, show me how to compute this.A random variable X is distributed according to pdf fx(x) given below fx (x) 1 -K K a) Find the value of K. b) Determine P(X > 1/2) c) Determine P(X > 0]x 1/2) ? e) What is the conditional expectation E{X | x > 1/2} ?
