The given probability distribution table is:

Here's how to solve the problem:

The given probability distribution table is:

$x$	3	25	$t$	$k$
$P(X=x)$	$\frac{3}{25}$	$\frac{1}{20}$	$\frac{1}{4}$	$k$

It is also given that $E(X) = \frac{101}{50}$.

a) The value of the constants $t$ and $k$

Step 1: Use the property that the sum of all probabilities in a distribution must equal 1.

$$\sum P(X=x) = 1$$ $$$$