This Quiz MCQs Probability Distributions for Random Variable covers the Mean and Variance of random variables and the distribution of Random variables. MCQs Probability Distributions quiz requires knowledge of events, experiments, mutually exclusive events, collectively exhaustive events, sure events, impossible events, addition and multiplication laws of probability, concepts related to discrete and continuous random variables, probability distribution and probability density functions, characteristics and properties of probability distributions, discrete probability distribution, continuous probability distributions, etc.

### MCQs Probability Distributions

- A family of parametric distribution in which the mean always greater than its variance is:
- The family of parametric distributions which has a mean always less than variance is:
- The family of parametric distributions for which moment generating function does not exist is:
- The distribution for which the mode does not exist is:
- The relation between the mean and variance of $\chi^2$ with $n$ degrees of freedom is
- The $F$-distribution curve with respect to tails is:
- If $X$ has a binomial distribution with parameter $p$ and $n$ then $\frac{X}{n}$ has the variance:
- The binomial distribution is symmetrical if $p=p=?$
- The shape of the Geometric distribution is
- If $X\sim N(\mu, \sigma^2)$ and $a$ and $b$ are real numbers, then mean of $(aX+b)$ is
- The distribution of sample correlation is
- Events having an equal chance of occurrence are called
- Studnet’s $t$-distribution curve is symmetrical about the mean, it means that
- The distribution possessing the memoryless property is
- The chi-square distribution is used for the test of
- The probability of failure in binomial distribution is denoted by
- In binomial distribution, the formula for calculating the mean is
- In binomial probability distribution, dependents of standard deviations must include
- The formula to calculate standardized normal random variables is
- The mean of a binomial probability distribution is 857.6 and the probability is 64% then the number of values of binomial distribution

Q#14 wrong

because

if mean is k then variance is 2k

k=2k

Mean = 2Variance

Thank you dear! for mentioning the error in quiz. More explanation is added to the question.

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The mean of a chi-square distribution is equal to its degrees of freedom ($k$) and the variance is $2k$.

It means that if Mean $=k=2$ then variance $= 2 times 2 = 4$

Therefore, $2, Mean = 2times 2 = 4 = , Variance$