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In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(x < 15) is
- a)1/2
- b)2/3
- c)1
- d)non
Correct answer is option 'A'. Can you explain this answer?
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In a discrete random variable x follows uniform distribution and assum...
Uniform Distribution:
In statistics, a uniform distribution is a probability distribution where all outcomes are equally likely. In other words, each value in the distribution has the same probability of occurring.
Given Information:
In this question, we are given that the random variable x follows a uniform distribution and assumes the values 8, 9, 11, 15, 18, and 20.
Determining the Probability:
We need to find the probability of x being greater than 15, i.e., P(x > 15).
To find this probability, we need to determine the number of favorable outcomes (values of x) and the total number of outcomes.
Favorable Outcomes:
From the given information, we can see that the values of x greater than 15 are 18 and 20. Therefore, there are 2 favorable outcomes.
Total Outcomes:
The total number of outcomes is the number of values x can assume, which is 6 in this case.
Calculating the Probability:
To calculate the probability, we divide the number of favorable outcomes by the total number of outcomes.
P(x > 15) = Number of Favorable Outcomes / Total Number of Outcomes
= 2 / 6
= 1/3
However, the question asks for P(x ≤ 15), not P(x > 15). Since the values of x are discrete and uniformly distributed, the probability of x being equal to 15 is 0.
Therefore, P(x 15) = 0.
The correct answer is option 'D' (non).
In statistics, a uniform distribution is a probability distribution where all outcomes are equally likely. In other words, each value in the distribution has the same probability of occurring.
Given Information:
In this question, we are given that the random variable x follows a uniform distribution and assumes the values 8, 9, 11, 15, 18, and 20.
Determining the Probability:
We need to find the probability of x being greater than 15, i.e., P(x > 15).
To find this probability, we need to determine the number of favorable outcomes (values of x) and the total number of outcomes.
Favorable Outcomes:
From the given information, we can see that the values of x greater than 15 are 18 and 20. Therefore, there are 2 favorable outcomes.
Total Outcomes:
The total number of outcomes is the number of values x can assume, which is 6 in this case.
Calculating the Probability:
To calculate the probability, we divide the number of favorable outcomes by the total number of outcomes.
P(x > 15) = Number of Favorable Outcomes / Total Number of Outcomes
= 2 / 6
= 1/3
However, the question asks for P(x ≤ 15), not P(x > 15). Since the values of x are discrete and uniformly distributed, the probability of x being equal to 15 is 0.
Therefore, P(x 15) = 0.
The correct answer is option 'D' (non).
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