The discrete random variable X has the probability distribution given by: 2 4 6 8 P(X= x) 0.15 0.15 2r 0.4 r a. Determine the following probability: P(X=4) = ? Answer in exact fraction or exact decimals b. What is the expected value of the random variable X? Answer in exact fraction or exact decimals c. What is the variance of the random variable X? Answer in exact fraction or exact decimals

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A: As per Bartleby guideline expert have to answer first three subparts only dear student please upload…

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A: The function is PDF if ∑pi=1 u2+0.05+0.35+u+0.15=13u2=920u=310=0.3

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A: Variance=EX2-E2(X)=22920+42120+5215+32310-2920+4120+515+33102=10.3-32=1.3

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A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks   For the…