A discrete random variable X has the following probability distribution: Value of X 1 2 3 4 5 6 Probability 0.30 0.20 0.15 0.15 0.10 0.10 Find the mean of the random variable X, μX. A) 4.15 B) 2.85 C) 3 D) 3.50 Find the variance of the random variable X, σ2X A) 2.8275 B) 1.3125 C) 3.4135 D) 1.9225 Find the standard deviation of the random variable X, σX.  A) 1.44 B) 1.68 C) 1.21 D) 1.89

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A: Given:

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A: a) From the given table  P(Y=1)=0.158

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Q: b) Use the theorem below to express E(W) = E(5Y) in terms of u, where u = E(Y). Let Y be a discrete…

A: Solution

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A: Given :   X=0 X=2 X=4 Y=1 0.03 0.02 0.1 Y=3 0.15 0.2 0.1 Y=5 0.2 0.15 0.05

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A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

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A:

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A: Expected value = E(X)

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Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Let X and Y be two discrete random variables with a joint probability distribution.     X=0 X=2…

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A: I solved exactly first three subparts because of bartleby policy if you want more please uplode…

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A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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A: Required probability is P(X≤-3 , Y≤0)

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A: We know that  Conditions for independent random variable x and y  f(x,y) = f(x) × f(y)

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A: For Y=2  Probabilities are given for every X, i.e. 0.04, 0.19, 0.05 So  P(Y=2)= 0.04+0.19+0.05= 0.28

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A:

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A: We know that the total probability is always 1.  So,  k+0.15+0.35+0.15+0.2+0.1=1

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Q: The table below gives the probability distribution of a discrete random variable X 1 2 3 4 5 1 17 19…

A: Since, the sum of all probabilities of a distribution is equal to 1. That means ∑P(x) = 1 a) The…

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A: Formula for the Variance of probability distribution is defined as below          V(X) = E(x2) –…

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Given Data:   x=0 x=2 x=4 y=1 0.03 0.02 0.1 y=3 0.15 0.2 0.1 y=5 0.20 0.15 0.05

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X =0 X-2…

A: Given,   X = 0  X =2 X =4 Y = 1 0.03 0.02 0.1 Y = 3 0.15 0.2 0.1 Y = 5 0.2 0.15 0.05

Q: Find the variance for the probability distribution X 4 0 1 2 3 P(X=x) 0.04 0.18 0.34 0.23 0.21…

A: Solution

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X = 0…

A: Here, X>0 means X=2 and X=4. And Y≤3 means Y=1 and Y=3.

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Given,   X=0 X=2 X=4 Y=1 0.03 0.02 0.1 Y=3 0.15 0.2 0.1 Y=5 0.2 0.15 0.05

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

A:

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

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