Question

2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3 times) a technician is called on an emergency call. The joint probability distribution fxy(x, y) is given by 1 0.05 0.05 0 0.05 0.1 0.2 0.1 0.35 0.1 (a) Evaluate the marginal pdf and the mean of X (b) Evaluate the marginal pdf and the mean of Y. (c) Evaluate P(Y = 3X = 2). (d) Evaluate E(XY) and determine if X and Y are uncorrelated.

Answer 1

Solution:- Let x be denote the number of times a certain numerical control machine will malfunction: 1, 2, or, 3 times on any given day. the Let y denote number of times a technician is caued on an emergency call. from exercise the joint Probability distribution is given as shown below, Scanned with CamScanner

f(x,y) 0.05 or - 0.05 2 3 Hly) 0.05 0.10 0.20 0.10 0.35 l 0.20 0.10 0.30 0.35 0.55 0.00 dfcx)wat fo.10 wit CamScanner 1

two random to be independent Now the objective is to find whether the Variables are dependent or independent: if f(, y) = f(x)+(y) then X and Y are said check whether fxy (1, 1) = fx (1). fx (1) or not. from the joint distribution table, tay (1, 1) =0.05 fall - $(11) + f(1/2) + f(13) 20.05+0.05 +0.00 fy (1) = f(1) (2,1) + f(31) -0.05+0.05 +0.10 -0.20 Now we consider, tow (!) .fy (I) = 0.10X6.20 20109 fxy (1.) & fx (1). fyll) Thertore , X andy are not independent . cs Scanned with CamScanner