Need solution step by step ThanksSolution4 Let us check diff

Need solution step by step

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Solution

4.

Let us check different values that V can take and their probabilities, such that we can finally find its probablity distribution.

(i) For X=0,Y=1, V=3*0*1=0

P(V₁=0) = P(X=0)*P(Y=1) = 0.3*0.8 = 0.24

(ii) For X=0 , Y=2 , V=3*0*2=0

P(V₂ =0) = P(X=0)P(Y=2) = 0.3*0.2=0.06

Thus since the first and second case both give the same values for V their probability should be added to give the probability of the random variable V when it takes the value 0. Thus,

P(V=0) = 0.24+0.06 = 0.30

(iii) For X=4, Y=1 , V=3*4*1=12

P(V=12) = 0.7*0.8 = 0.56

(iv) For X=4, Y=2, V=3*4*2 = 24

P(V=24) = 0.7*0.2 = 0.14

Thus now the probability distribution can be given as,

To find the variance first we have to find the mean.

E(V) = 0*0.30+12*0.56+24*0.14 = 10.08

Var(V) = (0-10.08)^2(0.30)+(12-10.08)^2(0.56)+(24-10.08)^2(0.14) = 59.6736

Please ask the 5th question separately.