5. Binomial Distribution & Discrete Random Variables
Discrete Random Variables
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A factory produces lightbulbs in batches of 50. The probability distribution for the number of defective lightbulbs in a randomly selected batch is shown below. Find the expected value.
A
0.17
B
1.7
C
0.03
D
2.5
Verified step by step guidance1
Understand the concept of expected value in probability distributions. The expected value is a measure of the center of the distribution, often referred to as the mean of the distribution.
Identify the random variable X, which represents the number of defective bulbs in a batch. The possible values of X are 0, 1, 2, 3, 4, and 5.
Recognize the probability distribution P(X) associated with each value of X. These probabilities are given as 0.20, 0.30, 0.25, 0.15, 0.07, and 0.03 respectively.
Use the formula for expected value: E(X) = Σ [x * P(x)], where x is a value of the random variable and P(x) is the probability of x occurring.
Calculate the expected value by multiplying each value of X by its corresponding probability and summing these products: E(X) = (0 * 0.20) + (1 * 0.30) + (2 * 0.25) + (3 * 0.15) + (4 * 0.07) + (5 * 0.03).
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