Probabilty Distribution Starter Quiz

Which of the following statement is/are correct?

I. The line of regression always passes through a point .

II. The value of coefficient of correlation lies between (-1, 1).

III. If the two regression lines are perpendicular to each other, then the coefficient of correlation is equal to zero.

IV. If two regression lines coincide each other, then the coefficient of correlation is ±1

The density function of a continuous random variable is given.

f(x) = 0    x < 2

      = k(2x + 3)    2≤ x ≤ 4

      = 0     > 4

Find P(2 ≤ x ≤ 3)

The probability density function of a continuous random variable is given by

The standard deviation will be

The number of corona positive people in a city in a month follows poisson distribution with mean of 7.8. find the probability that number of corona positive is less than 3 during a randomly selected month is

A librarian imposes 5 penalties a day for books not returned on time. If the penalties imposed follow Poisson distribution then the probability that there are less than 4 penalties a day is

If X is continuous random variable and its Probability distribution function is f(x)=e^–x, 0 < x < ∞

Then P(x ≤ 2) is _____.