1. Suppose that X is a continuous random variable whose probability density function is given by f(x)=C(4x-2x²)0 ≤x≤2 (Ootherwise a) What is the value of C? b) Find P{X>1}.

13. Suppose that the joint probability density of two random variables X₁ and X₂ is given by: J6e-2x₁-3x2 for x₁ > 0 and x₂ > 0, otherwise 0 f(X1.X2) = {6 Find the following probabilities. Show all steps. a) P(1 ≤X₁ ≤ 2, 2 ≤X₂ ≤3) b) P(X₁ 2).

Show that there are no values of c such that f(x) = cx can serve as the values of the probability distributionof a random variable with the countably infinite rangex = 1, 2, 3, ...

Let X1 and X2 be continuous random variables with the joint probability - function fx1,x,(x1, x2), -00 < x; < o, i = 1,2. Let Y1 = X1 + X2 and

Please answer all

The number of minutes that a flight from Phoenix to Tucson is early or late is a random variable whose proba-bility density is given by f(x) =⎧⎪⎨⎪⎩1288 (36 − x2) for −6 < x < 60 elsewhere where negative values are indicative of the flight’s beingearly and positive values are indicative of its being late.Find the probabilities that one of these flights will be(a) at least 2 minutes early;(b) at least 1 minute late;(c) anywhere from 1 to 3 minutes early;(d) exactly 5 minutes late.

EXERCISE 4. Suppose that X is a continuous random variable whose probability distribution function is given by c(4x- 2x)0 1).

Let X1 and X2 be discrete random variables with joint probability distribution x1 = 1, 2; x2 = 1, 2, 3, f(x1, x2) = 10, 18 elsewhere. Find the probability distribution of the random variable Y = X1X2.

For what values of k canf(x) = (1 − k)kx serve as the values of the probability distribution of arandom variable with the countably infinite range x =0, 1, 2, ...?

Q1) Determine the value c so that each of the following functions can ? serve as a probability distribution of the discrete random variable X f(x) = c (") (4 4 ),x = 0,1,2,3 %3D x |