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Aced
12.03.2020 •
Mathematics
Consider the following discrete probability distribution. x 15 22 34 40 P(X = x) 0.14 0.40 0.26 0.20 a. Is this a valid probability distribution? Yes, because the probabilities add up to 1. No, because the gaps between x values vary. b. What is the probability that the random variable X is less than 40?
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Ответ:
(a) Yes, because the probabilities add up to 1.
(b) The probability that X < 40 is 0.80.
Step-by-step explanation:
The probability distribution of the random variable X is:
x: 15 | 22 | 34 | 40
f (x): 0.14 | 0.40 | 0.26 | 0.20
(a)
The properties of a probability distribution are:
0 ≤ f (x) ≤ 1∑ f (x) = 1All the probability value are more than 0 and less than 1.
Compute the sum of all the probabilities as follows:
The sum of all probabilities is 1.
Thus, the probability distribution is valid.
(b)
Consider the probability distribution table.
Compute the probability of X < 30 as follows:
P (X < 40) = P (X = 15) + P (X = 22) + P (X = 34)
Thus, the probability that X < 40 is 0.80.
Ответ: