Fill in the P(X = x) values in the table below to give a legitimate probability distribution for the discrete random variable X, whose
possible values are 0, 1, 4, 5, and 6.
Value x of X P(X = x)
0 0.26
1 0.25
4 0.11
5
6

P (X = 5) = a and P (X = 6) = 0.38 - a

Step-by-step explanation:

The sum of probabilities of all the events in a sample space is known is 1.

That is:

It is provided that, the random variable X, can assume values 0, 1, 4, 5, and 6.

The incomplete probability distribution is:

X        P(X = x)

0          0.26

1           0.25

4           0.11

5             __

6            __

Compute the missing probabilities as follows:

Assume that P (X = 5) = a.

Here the value of a lies in the interval 0 ≤ a ≤ 0.38.

Then the value of P (X = 6) will be:

P (X = 6) = 0.38 - a

Thus, the complete probability distribution is:

X            P(X = x)

0              0.26

1               0.25

4               0.11

5                  a

6            0.38 - a

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