Please show your workings. Diane Bruns is the chairman of an enormous city. Recently, she has gotten worried about the likelihood that huge quantities of individuals who are drawing joblessness checks are furtively utilized. Her aides gauge that 40% of joblessness recipients fall into this class, yet Ms. Bruns isn't persuaded. She requests one from her helpers to lead a peaceful examination of 10 arbitrarily chose joblessness recipients. On the off chance that the city hall leader's aides are right, what is the likelihood that one or three of the researched people have occupations?

bank is keen on examining the quantity of individuals who utilize the ATM situated outside

its office late around evening time. By and large, 1.9 clients approach the ATM during any 10-minutes

span among 9pm and 12 PM. Distinguish the irregular variable in the above explanation and

recommend the suitable conveyance to investigate the idea of the irregular variable. Utilizing the

proposed answer, process the likelihood of precisely 4 clients utilizing ATM administrations in any

10 minutes span between 9 pm and 12 PM.

Likewise, process the likelihood of under 4 individuals utilizing the ATM during any 10 minutes

stretch between 9 pm and 12 PM.

A school teacher never completes his talk the hour's end and consistently completes his talks inside 2 min after the hour. Let X = the time that slips by between the hour's end and the finish of the talk and assume the pdf of X is as per the following:

f(x) = kx^2 if 0

(a) What is the likelihood that the talk proceeds past the hour for somewhere in the range of 30 and 90 sec? (Round your response to four decimal spots.)

~25~

(b) What is the likelihood that the talk proceeds for at any rate 105 sec past the hour's end? (Round your response to four decimal spots.)

Allow X to signify the measure of time a book on two-hour hold is really looked at, and assume the cdf is the accompanying. F(x) = 0 if x = 5. Utilize the cdf to get the accompanying. (On the off chance that important, round your response to four decimal spots.)

(d) What is the middle checkout span ? [solve 0.5 = F()]. (Answer isn't 3.536.)

(e) Obtain the thickness work f(x). (Answer is 2x/25.)

(f) Calculate E(X). (Answer isn't 3.333.)

For some constant c > 0, X and Y are bivariate Gaussian random variables with joint PDF exp ( (2 3) /4 (x-3)(y-1)/3+ (y-1)2/4 fx, x (x, y) = C 87 5/9 Let W = 2X + Y and R = X + Y. Choose all the true statements. Keep in mind that the number of true statements is random; it's possible that all 10 statements are true . Note that (z) is the CDF of the Standard Normal Random Variable Z, and Q (z) is the Standard Normal Complementary CDF. P(2X + Y 6) = Q(2/V3). The correlation coefficient px y = 1/3. The correlation coefficient PW , R = 0.782. Y is Gaussian (1, 4). Var W] = 92/3. W and R are bivariate Gaussian random variables. Cov W, R = 20. The constant c = 5/9.5. Consider a bivariate distribution with joint pdf given by 1 f(x, y) = cexp (ry+x ty' - 8x - 8y) , x,yER, where c is a normalizing constant. (a) By completing the square, or otherwise, show that the conditional distribution of X given Y = y is Gaussian with mean 4/(1 + y?) and variance 1/(1 + y?). [3 marks] Similarly, it can be shown that the conditional distribution of Y given X = x is Gaussian with mean 4/(1 + x2) and variance 1/(1 + a?). (b) Using the above results, or otherwise, describe how you could sample from the joint distri- bution f(x, y). [4 marks]As every Girl Scout knows, statistics teachers seriously love Girl Scout Cookies. The number of boxes of GS cookies statistics teachers order, like all important decisions made by statistics teachers, is determined by independent rolls of a 4-sided fair die. If a one appears, 6 boxes are ordered; if any other number appears, 2 boxes are ordered. a) What is the probability that a statistics teacher places an order for 2 boxes of Girl Scout cookies? b) What is the probability that with two independently chosen statistics teachers will each order 6 boxes each? c) What is the probability that for two independently chosen statistics teachers the first will order 6 boxes and the second will order 2 boxes? d) What is the probability that for two independently chosen statistics teachers exactly one will order 6 boxes