List of top Engineering Mathematics Questions on Probability and Statistics

If X is a Poisson random variable with variance \(P(X = 2) = 9 P(X = 4)\) then the mean and variance respectively are
If X and Y are independent random variables with variances \(\sigma_x^2 = 5\) and \(\sigma_y^2 = 3\) then the variance of the random variable \(Z = 3X + 2Y - 5\) is
Bag-I contains 4 white and 6 black balls, Bag-II contains 4 white and 3 black balls. A ball is selected at random and it comes out to be a black ball. What is the probability that it is from Bag-I?
Two fair dice are rolled, and the random variable \( X \) denotes the sum of the outcomes. What is the expected value of \( X \)?
The diameter of a fibre is assumed to be a continuous random variable \( X \) with probability density function \[ f(x) = 6x(1 - x), \quad 0<x \leq 1 \] If \( P(X<\beta) = P(X>\beta) \), then the value of \( \beta \) (rounded off to 1 decimal place) is _________.
Let \( X \) be a Poisson distributed random variable with parameter \( \lambda (> 0) \) such that it satisfies the equation \[ P(X = 1) = 3P(X = 3) - P(X = 2) {. Then, the value of } \lambda { is:} \]
The diameter of a fibre is assumed to be a continuous random variable \( X \) with probability density function \[ f(x) = 6x(1 - x), \quad 0<x \leq 1 \] If \( P(X<\beta) = P(X>\beta) \), then the value of \( \beta \) (rounded off to 1 decimal place) is _________.
Mean of a binomial distribution 12 and variance is 8. The probability of having at least one success is?

In large sample, the critical value for the single tailed test at 5% level of significance is?

For a bivariate data $(x_i, y_i)$ ($i=1,2,3,\dots,10$), $\sum x_i y_i = 6200$, $\sum x_i = 400$, $\sum y_i = 1220$, $\sum x_i^2 = 1800$, then equation of line of best fit is?
Let $X$ be a discrete random variable with probability mass function $P(X=x_i)$ where $x \in \{x_1, x_2, \dots, x_n\}$. If $\sum_{i=1}^{n} (x_i-2)^2 P(X=x_i) = 28$ and $\sum_{i=1}^{n} (x_i+2)^2 P(X=x_i) = 12$. Then variance of $X$ is?
If the probability density function of a continuous random variable X is $f(X=x) = Ke^{-3x}$, $0<x<\infty$, then a solution of $\frac{P^2+1}{P} = \frac{K}{\sqrt{2}}$ is?
If the mean and variance of a binomial variate are 12 & 4, then the distribution is _____
A continuous random variable \(X\) has a probability density function \( f(x) = 3x^2, \ 0 \leq x \leq 1 \). If \( P(X \leq a) = P(X>a) \), then the value of 'a' is
If the random variable \( X \) takes the values 1, 2, 3, and 4 such that \( 2P(X=1) = 3P(X=2) = P(X=3) = 5P(X=4) \), then the mean of \( X \) is
If $b_{yx}$ and $b_{xy}$ are regression coefficients and they are equal, then?
The probability density function is given by \( f(x) = \begin{cases} C(x-1), & \text{for } 1<x<4 \\ 0, & \text{otherwise} \end{cases} \). Find \(P(2<X<3)\).
Which of the following pairs of numbers is possible to be the regression coefficients for a data of two variables

The variance for continuous probability function \(f(x) = x^2 e^{-x}\) when \(x \ge 0\) is

Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for \(0 \le X \le 100\). The mean is
Probability that a leap year has 53 Sundays is
Probability Density function $f(x)$ of a continuous random variable is given by $f(x) = ce^{-|x|}, -\infty<x<\infty$. If the total probability $\int_{-\infty}^{\infty} f(x) dx = 1$ then $c =$
A problem of statistics is given to three students A, B and C whose chances of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that the problem will be solved?
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with the probability 0.2 then $P(A) + P(B) = $?

Which of the following probability distribution functions (PDFs) has the mean greater than the median?