Random Variables Calculator

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Example

Created on 2024-06-20Asked by Logan Allen (Solvelet student)

Find the expected value

E(X)

of a discrete random variable

X

with the following probability distribution:

\begin{array}{c|c} x_i & P(X = x_i) \\ \hline 1 & 0.2 \\ 2 & 0.3 \\ 3 & 0.4 \\ 4 & 0.1 \\ \end{array}

Solution

To find the expected value

E(X)

of a discrete random variable

X

: 1. Use the formula for expected value:

E(X) = \sum_{i} x_i P(X = x_i).

2. Substitute the given values into the formula:

E(X) = 1 \cdot 0.2 + 2 \cdot 0.3 + 3 \cdot 0.4 + 4 \cdot 0.1.

3. Simplify:

E(X) = 0.2 + 0.6 + 1.2 + 0.4 = 2.4.

Therefore, the expected value

E(X)

is 2.4. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Ella Smith on Solvelet

1. Calculate the expected value of a random variable with a probability distribution given by

P(X = 1) = 0.2

P(X = 2) = 0.5

, and

P(X = 3) = 0.3

.2. Find the variance of a random variable with a probability distribution given by

P(X = -1) = 0.3

and

P(X = 1) = 0.7

DefinitionRandom variables are the numerical outcomes of random events. They can be Just a specific or individual values (called Discrete) or any values within a range (Continuous). Heads in 10 coin flips (discrete random variable) vs. height of students in a class (continuous random variable) if our random variable is counts(#) then it is discrete, heights( 4f,4.11 fts) as we can see our random variable is quantitative and it is not countable.

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