Solved: The probability mass function (PMF) for the random…

Here's the solution to your probability problem.

The probability mass function (PMF) for the random variable $Y$ is given by the table:
$Y$ : 0, 1, 2, 3, 4
$P(Y)$ : $\frac{1}{8}$ , $2k$ , $\frac{1}{6}$ , $3k$ , $\frac{2}{7}$

I) Find the value of $k$

The sum of all probabilities in a PMF must equal 1.
$\sum P(Y=y) = 1$ $\frac{1}{8} + 2k + \frac{1}{6} + 3k + \frac{2}{7} = 1$
Combine like terms and fractions.
$5k + \left(\frac{1}{8} + \frac{1}{6} + \frac{2}{7}\right) = 1$

The probability mass function (PMF) for the random variable Y is given by the table:

Step-by-step solution

The sum of all probabilities in a PMF must equal 1.

Combine like terms and fractions.

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