(2 points) Let X1, X2 be 2 mutually independent discrete random variables. The f
ID: 3064957 • Letter: #
Question
(2 points) Let X1, X2 be 2 mutually independent discrete random variables. The first variable X1 can be a whole number from 1 to 5. Its distribution function is m,(i) = 6-i 15 The second variable X2 can be a whole number from 1 to 6. It has a uniform distribution. First, find the exact values (using fractions) of P(X 42/15 P(X,-5-15 P(X1 = 4 and X2 = 5) =| 275 Let Y denote the maximum of the Xf's. Find the probability that Y-1: P(Y= 1) = 1/15 Find the probability that Y 2, P(Y = 2) =| 1375 Hint: Use cases based on what X1 and X2 are.Explanation / Answer
here P(X1 =4 )=(6-4)/15 =2/15
P(X2=5) =1/6 (as there are 6 variables and each has equal probability))
P(X1=4 ; X2=5) =(2/15)*(1/6) =2/90 =1/45
P(Y=1) =P(X1=1; X2=1)=(5/15)*(1/6) =1/18
P(Y=2) =P(X1=2; X2=1)+P(X1=1; X2=2)+P(X1=2; X2=2) =(4/15)*(1/6)+(5/15)*(1/6)+(4/15)*(1/6)=13/90
( please revert if any answer mismatches or clarification)
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