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- Actuary Tong has to study for two actuarial exams: Exam P and Exam FM. The amount of study time that Actuary Tong will spend on each exam in a day follows a continuous random variable that ranges from o to i hour. The amount of study time that Actuary Tong spends on both exams in a day has a joint density function that is equal to the sum of the study times that Actuary Tong spends on ench exam in a day. Caleulate the probability Actuary Tong spends at least half an hour in a day studying for exactly one of the exams. A 0.45 B 0.50 0.55 D 0.60 0.65 REPSuppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.Let X be a continuous random variable with pdf
- Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.If a dealer’s profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function Find the variance of X.Let X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.
- Let X1 and X2 be two continuous random variableshaving the joint probability density f(x1, x2) = 4x1x2 for 0 < x1 < 1, 0 < x2 < 10 elsewhereFind the joint probability density of Y1 = X21 and Y2 = X1X2.Show that the probability density function of a negative binomial random variable equals theprobability density function of a geometric random variable when r = 1. Show that the formulasfor the mean and variance of a negative binomial random variable equal the corresponding resultsfor a geometric random variable when r = 1.Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1 0; elsewhere } What is the joint CDF of X and Y?