The second worksheet is the pdf of a random variable U, presented as a tabled probability distribution. This can be called a probability model of the random variable U in a population. Compute the population variance of the random variable U, given the probability model of it presented in the second worksheet.   u P(u) 0 0.3 1 0.1 2 0.1 3 0.1 4 0.05 5 0.05 6 0.05 7 0.05 8 0.05 9 0.05 10 0.05 11 0.05

Q: P(x, y) 1 0.010 0.015 0.025 1. 0.020 0.030 0.050 0.050 0.075 0.125 3 0.060 0.090 0.150 4 0.040 0.060…

A:

Q: The marginal distributions of two random variables X and Y, together with some values of their joint…

A: Solution-: We have following table:   Y=1 Y=2 Y=3 Total X=1 - 0.08 - 0.20 X=2 - 0.32 - 0.80…

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

A: 20 0.3 6 400 120 30 0.05 1.5 900 45 40 0.4 16 1600 640 50 0.15 7.5 2500 375 60 0.1 6 3600…

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Q: the probability mass function of a discrete random variable X representing the number of bicycles…

A: Formula : Variance = E(X^2) - [E(X)]^2

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Q: Define the indicator variable IA of a random event A, and show that E(IA) = P(A).

A: We have to define the indicator variable IA of a random event A, and also to show that EIA=PA.

Q: The joint probability distribution of the number X of cars and the number Y of buses per signal…

A:

Q: 18) Find the variance for the given probability distribution. x | P(x) 0 0.19 1 0.33 2 0.31 3 0.09 4…

A: Step 1:Step 2: Step 3: Step 4:

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Q: table in such a way that X and Y are dependent random variables. Y= -3 Y=-1 Y=0 X=-2 0.01 0.10 X=-1…

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A: We know that, If X and Y are independent random variables.  Var(X+Y)= Var(X)+ Var(Y)

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A: Probability distribution is,   x p(x) 1 0.10 2 0.60 3 0.15 4 0.10 5 0.05

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A: Cov(X,Y)=E(XY)-E(X)E(Y)corr(X,Y)=Cov(X,Y)V(X)V(Y)

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Q: The marginal distributions of two random variables X and Y, together with some values of their joint…

A: Solution-: We have following table:   Y=0 Y=1 Y=3 Total X=1   0.06   0.60 X=3   0.04   0.40…

Q: y p(x, y) 2 0.015 0.010 0.025 0.030 0.020 0.050 2 0.075 0.050 0.125 0.090 0.060 0.150 4 0.060 0.040…

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Q: f(x|p) = p(1-p)²-1 for x = 1, 2, 3, ... and 0 < p < 1. a) Give the likelihood function of p? b)…

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