3. Suppose that X is normally distributed N(3.6,0.81).IfY a. Find the probability density functio...
3. Suppose that X is normally distributed N(3.6,0.81).IfY a. Find the probability density function for Y b. State the mean and the expected value for Y c. Calculate the probability P(120S YS 520).
Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is given by fx)-[e(1+3) sxs2 otherwise (a) Find the value of c. (b) Find the mean and variance (c) Find P(1 <x<2.25) (d) Find the cumulative distribution function.
1. This question is on probability a. Suppose that X is a normally distributed random variable, where X N (M, o). Show that E [cºX f (x)] = cºu+20oʻE [ f (x + 002)] where f is a suitable function and 0 € R is a scalar. Hint: Write X = 1 +o0; 0~ N (0,1) and calculate the resulting integral b. Consider the probability density function X>0 p(x) = { Az exp (-1.2-2) 10 x < 0 (>0) is...
Suppose the rv Y is normally distributed with mean -2 and variance 25 (a) Find the probability that Y exceeds 1, given that Y is positive. (b) Find the expected value of Y, given that Y is positive. Hint: For (b), first derive the cdf of the rv given by X = (Y | Y > 0). (Please don't copy and paste)
Please answer this question Suppose X is normally distributed with mean 1 and standard deviation 0.25, and Y... Suppose X is normally distributed with mean 1 and standard deviation 0.25, and Y is also normal with mean 1.5 and standard deviation 0.4. Suppose that X and Y have correlation coefficient 0.6. Find the following probabilities: (a) P(X 2 1.3) (b) P(X+y-2.5) (c) P(X +Y 2 3) (d) P(Y - X so) (e) P(Y <X)
Exercise 4 (Continuous Probability) For this exercise, consider a random variable X which is normally distributed with a mean of 120 and a standard deviation of 15. That is, x-.. N (μ = 120, σ. 225) (a) Calculate P(X<95) (b) Calculate P(X > 140) c) Calculate P(95<X<120 (d) Find q such that P(X<)-0.05 (e) Find q such that P(X>) 0.10
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
3. Let X be a standard normally distributed random variable with probability density p(x)eT. Show that: a. EX0 b.1. (Hint: integration by parts will help you reduce this to part (a).) c. Eletx-ет, t2
1. Let X and Y be continuous random variables with joint pr ability density function 6e2re5y İfy < 0 and x < otherwise. y, fx,y (z,y) 0 (a) [3 points] Show that the marginal density function of Y is given by 3es if y 0, 0 otherwise. fy (y) = (b) |3 poin s apute the marginal density function of X (c) [3 points] Show that E(X)Y = y) =-y-1, for y 0 (d) 13 points] Compute E(X) using the...
If X is Normally distributed with a mean of 3 and a variance of 4, find P(|X−3|>1.6) to 2 decimal places. The probability is: