Q.2) (a) Show that the following function satisfies the properties of a joint probability mass function. 1/4 1/8 1/4 1/4 1/8 1 1.5 1.5 2.5 3 Determine the following. (b) The marginal probability distribution of the random variable X. (c) The conditional probability distribution of Y given that X-1.5. (d) Are X and Y independent? Support your answer by calculation.

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A: Let  be a random variable with the following probability distribution.Value x of…

Q: Let X be a random variable with the following probability distribution. Question table Value x of X…

A: E[X] = ∑xP(x)

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A: Solution

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A: Let X be the random variable having probability distribution is,  X P(X=x)  30 0.45 40 0.15…

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A: Here given discrete probability distribution of X.Use formula of expected value and Variance

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A: It is given that X is the random variable in probability distribution.

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A: The given data is,

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A: Consider the preliminary calculations given below: Value x of…

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A: E(X)=∑X.P(X)E(X2)=∑X2.P(X)V(X)=E(X2)-(E(X))2

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A: The joint probability distribution of random variables X and Y is given…

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A: X (X=x)  3 0.35 4 0.40 5 0.15 6 0.10 Then,  Expectation of X E(X) and variance of X…

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A: Answer X          P[x] 20       0.1530       0.2040       0.1050       0.1060       0.1070…

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A: Let's tackle each part of the problem: (a) List the values X may assume: The values X may assume are…