# Section 4.2. Probability Distributions for Discrete RandomVariablesExercise 2. Determine whether or not the table is a valid probability distribution of adiscrete random variable. Explain fullya.0.250.500,350,100.30b.0.3250.4060,164C.260.2727280.18290,140.13Exercise 4. A discrete random variable X has the following probability distribution:240.17270.16200,220.250,20Compute each of the following quantitiesa. P(18)b. P(X> 18)c, P(X 18)d, The mean μ of Xe. The variance σ2 of Xf. The standard deviation σ of X

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Step 1

Hello there ! I see that there are more than one questions here. Accoding to our policies cannot answer more than one question. So do find the solution to Exercise 2.

Step 2

Given a distribution of a discrete random variable. We need to check it if it is valid probability distribution or not.

A distribution is valid probability distribution if and only if All P(Xi) ≥ 0 and   ∑P(Xi) = 1.

Here the first distribution is shown below

Here all probabilities are not greater than or equal to 0. We see P(X=0) = -0.25. This is not possible, So we say that this is not a valid probability distribution.

Step 3

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