The given probability distribution table is:

April 26, 2026Mathematics

ScanSolve AI Answer

April 26, 2026

Answer

\frac{101}{50}$.

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

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Here's how to solve the problem: The given probability distribution table is: | x | 3 | 25 | t | k | |---|---|---|---|---| | P(X=x) | (3)/(25) | (1)/(20) | (1)/(4) | k | It is also given that E(X) = (101)/(50).

Asked on April 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 26, 2026

Here's how to solve the problem: The given probability distribution table is: | x | 3 | 25 | t | k | |---|---|---|---|---| | P(X=x) | (3)/(25) | (1)/(20) | (1)/(4) | k | It is also given that E(X) = (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. P(X=x) = 1