X is a uniformly distributed continuous random variable. If the mean and the variance of X are 5 and 4/3 respectively, find P[X>4].

P[X>4] = 0.875

Step-by-step explanation:

Random Variable = X

Mean of variable = 5

Variance of variable = 4/3

Required = Find the probability that X is greater than 4

The variance is a measure of dispersion while the mean is a measure of central tendency.

Variance = 4/3 = 1.333

[5 - 1.333] , [5 + 1.333]  =  [3.667 , 6.333]

The probability that X>4 is same as the probability that X lies between 4.001 and 6.333

The figure 4.001 is used because X is a continuous variable; it can take on even the most minute values within its range. So if X will be greater than 4, it doesn't have to be 5 or 4.1 ; it can be any value between 4 and 4.1 . For this analysis, 3d.p. (three decimal places) is used, so the next larger number after 4.000 is 4.001 .

6.333 - 3.667 = 2.666

4.000 - 3.667 = 0.333

This makes the probability that X is between the lower limit and 4.000 = 0.333/2.666 = 0.125

6.333 - 4.001 = 2.332

This makes the probability that X is between 4.001 and the upper limit = 2.332/2.666 = 0.875

This is the probability that the continuous random variable X is greater than 4.0

In figures, P[X>4] = 0.875

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step-by-step explanation: