Let A and B have the joint probability density function f(a,b) = 6(1-a - b) for a+b < 1, a>0, b>0 and it is zero elsewhere Calculate for expected value of (AB + 2A^2)
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Solve using the marginal of X and Y
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- For the continuous probability function f (x) = Kx² e* when x20 fint i) k i) mean iii) varianceThe life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by ´2e-(x+2) x 2 0, y 20 fx,y(x,y)=| else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.3935 b. 0.606 c. 0.7772 d. 0.3669 e. 0.6318Suppose 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 and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.Let X ~ Uniform(a, b). Find Expected value EX.The continuous random variable XX has a probability density function (pdf) given by Part(d) Find Var(X), correct to 2 decimal places Part(e) Find the median of X, correct to 2 decimal places.Part(f) Find E(X), correct to 2 decimal places
- A random variable X has the probability density function as f(x) = Ax(9-X2) 0 ≤ x ≤ 3 = 0 otherwise Find the value of A, the mean and the standard deviation of X.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 REPFind the probability that the student is female, given that an education degree is not received. P(F|E')
- As soon as possible! Let X and Y be continuous random variables with joint PDFFigure I shows the piecewise function (I), (II), (III) and (IV) for cumulative distribution function F(x) for continuous random variable. F(x) (6. 1) IV III II (4.0.8333) (0.0.1667) Figure I Construct the probability density function fix). Should one of the piecewise functions (IV) is not constant, explain the changes.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.
