In a binomial distribution, the sum of its mean and variance is 1.8. If the event was conducted 5 times, then the probability of 3 successes is

If the probability distribution of X is :

Then variance is equal to :

Which of the following statements are correct?

(A) The mean of a binomial distribution is always greater than the variance.

(B) The mean of a Poisson distribution is always greater than the variance.

(C) If $f(x)$ is the probability density function of a random variable $X$, then $P(a \leq X \leq b) = \int_a^b f(x)dx$.

(D) If $X$ is a random variable and $a,b$ are real numbers, then $Var(aX+b)=a^2Var(X)$.

Choose the correct answer from the options given below:

Ajay is a vendor who informs that there are 2% rotten apples in the fruit bag. Find the probability that a sample of 10 apples will include not more than one rotten apple.

If a random variable X follows binomial distribution with mean $\dfrac{4}{3}$ and variance $\dfrac{8}{9}$. Which of the following are correct?

A. Probability of success is $\dfrac{1}{3}$.

B. Probability of failure is $\dfrac{2}{3}$.

C. Number of trials is 4.

D. $P(X \ge 1) = \dfrac{35}{81}$

Choose the correct answer from the options given below:

If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :

A traffic police officer records the number of motorcycle riders that use a particular lane on a highway. He records that an average of 2.5 motorcycle riders use the lane every hour. Given that the number of motorcycles that use the particular lane follows a Poisson distribution. The probability that less than 2 motorcycle riders will use the lane within an hour will be:- (Use $e^{2.5} = 12.2$)