Question

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

Answer 1

Answer:

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:

$\sum\limits^{n}_{i=1}[P(X=x_{i})]=1$

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:

$\sum\limits^{n}_{i=1}[P(X=x_{i})]=1$

$P(X=0)+P(X=1)+P(X=4)+P(X=5)+P(X=6)=1\\\\0.26+0.25+0.11+P(X=5)+P(X=6)=1\\\\0.62+P(X=5)+P(X=6)=1\\\\P(X=5)+P(X=6)=1-0.62\\\\P(X=5)+P(X=6)=0.38$

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