PROBABILITY DISTRIBUTIONS

Which of the following statements is true?

• Mean and Variance of Binomial Distribution are equal

• Mean and Variance of Poisson's Distribution are equal

• Mean and Variance of Poisson's and Exponential Distribution are equal

• Mean and Variance of Normal Distribution are equal

Answer explanation

Mean and Variance of Poisson's distribution = λ

Find f(2) in normal distribution if mean is 0 and variance is 1.

• 2.718

• 0.1468

• 0

• .0305

Find λ in Poisson’s distribution if the probabilities of getting a head in biased coin toss as 3/4 and 6 coins are tossed.

• 4.5

• 3

• 1.125

• .045

Answer explanation

p = ³⁄₄
λ = np = (6) ³⁄₄ = 4.5.

If the probability that a bomb dropped from a place will strike the target is 50% and if 10 bombs are dropped, find mean and variance?

• 2 & 0.5 respectively

• 0.5 & 2.5 respectively

• 5 & 2.5 respectively

• None

Answer explanation

n = 10, p= 0.5, q = 0.5 then mean = np = 10*0.5 = 5. Var = npq = 2.5

If the average time between two events following an exponential distribution is 4 minutes, what is the rate parameter?

• 0.25

• 0.5

• 4

• 1

Calculate the variance of the exponential distribution with a rate parameter of 0.3.

• 11.1

• 0.09

• 0.3

• 0.18

Total Probability covered under any probability curve is

• 0.5

• ∞

• 0

• 1

μ = 70 , σ = 8 , X = 50 . Find z score

• 5.5

• 2.5

• -5.5

• -2.5

What is the standard deviation of a normal distribution with a mean of 50 and variance of 25?

• 5

• 25

• 50

• 125

For a normal distribution, what percentage of data falls within 3 standard deviations of the mean?

• 68%

• 95%

• 99.7%

• 100%