Question Solved1 Answer 6. Let X, Y, Z be independent and uniformly distributed over (0, 2). Compute P(x > YZ). 7. Consider two random variables X and Y with joint PMF given in table Y = 2 Y = 4 Y = 5 X = 1 } X = 4 be i 6 1 (a) Find P(X < 2, Y < 4) (b) Find the marginal PMFs of X and Y. (c) Find P(Y = 2 X = 1). (d) Are X and Y independent? 15:26 V

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Transcribed Image Text: 6. Let X, Y, Z be independent and uniformly distributed over (0, 2). Compute P(x > YZ). 7. Consider two random variables X and Y with joint PMF given in table Y = 2 Y = 4 Y = 5 X = 1 } X = 4 be i 6 1 (a) Find P(X < 2, Y < 4) (b) Find the marginal PMFs of X and Y. (c) Find P(Y = 2 X = 1). (d) Are X and Y independent? 15:26 V
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Transcribed Image Text: 6. Let X, Y, Z be independent and uniformly distributed over (0, 2). Compute P(x > YZ). 7. Consider two random variables X and Y with joint PMF given in table Y = 2 Y = 4 Y = 5 X = 1 } X = 4 be i 6 1 (a) Find P(X < 2, Y < 4) (b) Find the marginal PMFs of X and Y. (c) Find P(Y = 2 X = 1). (d) Are X and Y independent? 15:26 V
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Solution[7] Given the joint PMR table for X and Y[a]{:[P(x <= 2","y <= 4)=P(x=1","y=2)+P(x=1","y=4)],[=(1)/(3)+(1)/(24)=(9)/(24)=(3)/(8)],[P(x <= 2","y <= 4)=(3)/(8)]:}[b] Marginal pinf of xMarginal pmf of Y[c] p(Y=2∣x=1)=(p ... See the full answer