Question

initial knowledge check question 14 fill in the $p(x = x)$ values to give a legitimate probability distribution for the discrete random variable $x$, whose possible values are 2, 3, 4, 5, and 6. values $x$ of $x$ | $p(x = x)$ 2 | 0.23 3 | 0.25 4 | 0.23 5 | 6 |

Explanation:

Step1: Sum known probabilities

$0.27 + 0.26 + 0.23 = 0.76$

Step2: Calculate remaining total probability

$1 - 0.76 = 0.24$

Step3: Distribute remaining probability

Note: For a valid distribution, the two missing probabilities must be non-negative and sum to 0.24. A simple valid split is equal values:
$\frac{0.24}{2} = 0.12$

Answer:

For $x=5$, $P(X=x)=0.12$; for $x=6$, $P(X=x)=0.12$
(Any non-negative values for the two missing probabilities that add up to 0.24 are acceptable, this is one valid solution.)