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
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 that the probability distribution is given, with P(X) values corresponding to each X value: P(0) = 0.20, P(1) = 0.30, P(2) = 0.25, P(3) = 0.15, P(4) = 0.07, and P(5) = 0.03.
The expected value (E[X]) of a discrete random variable is calculated using the formula: E[X] = Σ [x * P(x)], where the sum is over all possible values of x.
Substitute the given values into the formula: E[X] = (0 * 0.20) + (1 * 0.30) + (2 * 0.25) + (3 * 0.15) + (4 * 0.07) + (5 * 0.03).
Calculate each term in the sum and then add them together to find the expected value of the number of defective bulbs in a batch.
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