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A discrete random variable x follows uniform distribution and takes the values 6, 8, 10, 12, 18
Q. The probability of P( x < 12) is
- a)1/5
- b)4/5
- c)3/5
- d)none
Correct answer is option 'C'. Can you explain this answer?
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A discrete random variable x follows uniform distribution and takes th...
Uniform Distribution and Probability Calculation
Uniform Distribution
Uniform distribution is a probability distribution in which all possible outcomes are equally likely. It is also known as rectangular distribution.
In a uniform distribution, the probability of an event occurring is the same for every possible outcome.
Probability Calculation
The probability of an event is the measure of the likelihood that the event will occur. It is a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
The formula for calculating probability is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Problem
A discrete random variable x follows uniform distribution and takes the values 6, 8, 10, 12, 18Q. The probability of P(x≥12) is
(a) 1/5
(b) 4/5
(c) 3/5
(d) none
Solution
Given, x follows uniform distribution and takes the values 6, 8, 10, 12, 18Q.
The probability of each outcome is:
P(x=6) = 1/5
P(x=8) = 1/5
P(x=10) = 1/5
P(x=12) = 1/5
P(x=18Q) = 1/5
The probability of P(x≥12) is the sum of probabilities of x=12 and x=18Q.
P(x≥12) = P(x=12) + P(x=18Q)
P(x≥12) = 1/5 + 1/5
P(x≥12) = 2/5
The probability of P(x≥12) is 2/5.
Therefore, the correct answer is option (c) 3/5.
Uniform Distribution
Uniform distribution is a probability distribution in which all possible outcomes are equally likely. It is also known as rectangular distribution.
In a uniform distribution, the probability of an event occurring is the same for every possible outcome.
Probability Calculation
The probability of an event is the measure of the likelihood that the event will occur. It is a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
The formula for calculating probability is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Problem
A discrete random variable x follows uniform distribution and takes the values 6, 8, 10, 12, 18Q. The probability of P(x≥12) is
(a) 1/5
(b) 4/5
(c) 3/5
(d) none
Solution
Given, x follows uniform distribution and takes the values 6, 8, 10, 12, 18Q.
The probability of each outcome is:
P(x=6) = 1/5
P(x=8) = 1/5
P(x=10) = 1/5
P(x=12) = 1/5
P(x=18Q) = 1/5
The probability of P(x≥12) is the sum of probabilities of x=12 and x=18Q.
P(x≥12) = P(x=12) + P(x=18Q)
P(x≥12) = 1/5 + 1/5
P(x≥12) = 2/5
The probability of P(x≥12) is 2/5.
Therefore, the correct answer is option (c) 3/5.
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A discrete random variable x follows uniform distribution and takes the values 6, 8, 10, 12, 18Q.The probability of P( x 12) isa)1/5b)4/5c)3/5d)noneCorrect answer is option 'C'. Can you explain this answer?
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