Bruce Sherman
2022-10-02
Answered

Find k for the following probability distributions: P(x) = k(x + 2) for x = 1, 2, 3

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tiepidolu

Answered 2022-10-03
Author has **8** answers

Given:

P(x)=k(x+2)

x=1,2,3

We need to determine the unknown value of k.

A probability distribution needs to satisfy two properties:

All probabilities need to be between 0 and 1 (including).

The sum of the probabilities of all possible outcomes needs to be equal to 1.

Note that we can use the second property to determine the unknown value of k.

Let us evaluate the given formula for P(x) at all possible values for x.

P(1)=k(1+2)=3k

P(2)=k(2+2)=4k

P(3)=k(3+2)=5k

The sum of all given probabilities needs to be equal to 1.

3k+4k+5k=1

12k=1 Combine like terms

$$k=\frac{1}{12}$$ Divide each side by 12

Thus we have derived that the unknown value of k is $$\frac{1}{12}$$.

Result:

$$k=\frac{1}{12}$$

P(x)=k(x+2)

x=1,2,3

We need to determine the unknown value of k.

A probability distribution needs to satisfy two properties:

All probabilities need to be between 0 and 1 (including).

The sum of the probabilities of all possible outcomes needs to be equal to 1.

Note that we can use the second property to determine the unknown value of k.

Let us evaluate the given formula for P(x) at all possible values for x.

P(1)=k(1+2)=3k

P(2)=k(2+2)=4k

P(3)=k(3+2)=5k

The sum of all given probabilities needs to be equal to 1.

3k+4k+5k=1

12k=1 Combine like terms

$$k=\frac{1}{12}$$ Divide each side by 12

Thus we have derived that the unknown value of k is $$\frac{1}{12}$$.

Result:

$$k=\frac{1}{12}$$

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