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- Suppose the variables Q and W are skewed distributions defined over a limited set of values. What is the probability that W takes on a value between 0.5 and 1.75? What is E(W)? Suppose that the domain of W changes to 0<t<2.5, what happens to the Probability Density Function (PDF)?Suppose you choose at random a real number X from the interval [2, 10]. (a) Find the density function f(x) and the probability of an event E for this experiment, where E is a subinterval [a, b] of [2, 10].(b) From (a) find the probability that X > 5, that 5 < X < 7, and that X2−12X +35 >0.Suppose that the joint probability density function of X and Y is fX,Y(x,y) = 10.125(x2 – y2) e−3x , for 0<x<∞ and -x<y<x 0, otherwise Give your answers to the below questions in two decimal places where appropriate. (a) The marginal probability density function of X is given by: fX(x) = A xB e-3x , for 0<x<∞ 0, otherwise Find the value of A. (b) Find the value of B. (c) The conditional probability density function of Y, given that X=x for some x>0, takes the following form: fY|X=x(y) = C (x2-y2) xD e-Ex, for -x<y<x 0, otherwise. Find the value of C (d)Find the value of D. (e)Find the value of E.
- a. Find the 50-th percentile of X. That is to say the value of x such that P (X ≤ x) = 0.5. b. Now say you have two independent jet engines. What is the probability that only one of themwill last more than 12 months before needing to be rebuilt? c. Find the probability density function f(x) by taking the derivative of F(x) with respect to x.Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx5; [0, 6]