Suppose that the random variable X represents th If E(X) 9 and V(X) 0.25, wh millimeters. Meani Variance mm mm²

Suppose X is a random variable of a normal distribution with E(X)=2 and Var(X)=4. Find P(X<4)

Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)

If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.

A persons blood glucose level and diabetes are closely related XB a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Supposed to after a 12 hour fast the random variable X will have a distribution that is approximately normal with mean of u=87 and a standard deviation of O=25. Note: after 50 years of age both the mean and Standard deviation tends to increase for an adult under 50 after 12 hour fast find the following probabilities A) X is more than 60 B) X is less than 60 C) X is between 60 and 110 D) X is greater than 125 (borderline diabetes starts at 125)

Let L be the random variable for the length of time, in years, that a person will remember an actuarial statistic. For a certain popula- tion, L is exponentially distributed with mean 1/Y, where Y has a gamma distribution with a = 4.5 and 3 = 4. Find the variance of L.

USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees. (a) Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.) A.  P(0) =  P(1) =  P(2) =  P(3) =  P(4) =  (c) What is the expected number of parolees in Alice's group who will not be repeat offenders? paroleesWhat is the standard deviation? (Round your answer to two decimal places.) parolees(d) What is the smallest group Alice can counsel to be at least 98% sure that three or more parolees will not become repeat offenders? parolees

Suppose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square distribution with 2 degrees of freedom.

Q13 b and c pls, thank you. Mean = 1/500 = 0.002var(x) = 1/500^2 = 0.000004