Math  /  Data & Statistics

QuestionFind the expected value E(X)E(X) of the following data. Round your answer to one decimal place. \begin{tabular}{|c|c|c|c|c|c|} \hlinexx & 2 & 3 & 4 & 5 & 6 \\ \hlineP(X=x)P(X=x) & 0.1 & 0.1 & 0.3 & 0.2 & 0.3 \\ \hline \end{tabular}
Answer How to enter your answer (opens in new window) Tables Keybc

Studdy Solution

STEP 1

1. The variable XX is a discrete random variable taking values 2,3,4,5,62, 3, 4, 5, 6.
2. The probabilities associated with each value of XX are given as P(X=2)=0.1P(X=2) = 0.1, P(X=3)=0.1P(X=3) = 0.1, P(X=4)=0.3P(X=4) = 0.3, P(X=5)=0.2P(X=5) = 0.2, and P(X=6)=0.3P(X=6) = 0.3.
3. The expected value E(X)E(X) is calculated using the formula for the expectation of a discrete random variable: E(X)=ixiP(X=xi)E(X) = \sum_{i} x_i P(X=x_i).
4. The final answer should be rounded to one decimal place.

STEP 2

1. List the values of XX and their corresponding probabilities.
2. Multiply each value of XX by its corresponding probability P(X=x)P(X=x).
3. Sum the products obtained in the previous step to find the expected value E(X)E(X).
4. Round the result to one decimal place.

STEP 3

List the values of XX and their corresponding probabilities.
xP(X=x)20.130.140.350.260.3 \begin{array}{|c|c|} \hline x & P(X=x) \\ \hline 2 & 0.1 \\ 3 & 0.1 \\ 4 & 0.3 \\ 5 & 0.2 \\ 6 & 0.3 \\ \hline \end{array}

STEP 4

Multiply each value of XX by its corresponding probability P(X=x)P(X=x).
20.1=0.230.1=0.340.3=1.250.2=1.060.3=1.8 2 \cdot 0.1 = 0.2 \\ 3 \cdot 0.1 = 0.3 \\ 4 \cdot 0.3 = 1.2 \\ 5 \cdot 0.2 = 1.0 \\ 6 \cdot 0.3 = 1.8

STEP 5

Sum the products obtained in the previous step to find the expected value E(X)E(X).
E(X)=0.2+0.3+1.2+1.0+1.8=4.5 E(X) = 0.2 + 0.3 + 1.2 + 1.0 + 1.8 = 4.5

STEP 6

Round the result to one decimal place. Since the result is already at one decimal place, no further rounding is needed.
E(X)=4.5 E(X) = 4.5
The expected value E(X)E(X) is 4.54.5.

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