List of top Statistics Questions

Let $G_x(\cdot)$ be the distribution function of an arbitrary random variable symmetric about $0$ (zero) and $G_x^{\leftarrow}$ is the inverse function of $G_x$ then for $p \in (0, 1)$ value of $G_x^{\leftarrow}(p) + G_x^{\leftarrow}(1-p)$ is

If $G(x)$ be the distribution function of random variable $X$ symmetric about $0$ then $\int_{-a}^{a} G(x)dx$ equals

If $X, X_1, X_2$ are independent and identically distributed positive random variables with distribution function $F_X(x)$ then $\int_{0}^{\infty} 2 \cdot x \cdot \overline{F}_X^2(x) dx$ equals

Let $X_{1}, X_{2}$ be independent random variables each from a discrete probability mass function $P_{X}(x) = \begin{cases} 1/3 & \text{if } x = 0 \\ 2/3 & \text{if } x = 1 \end{cases}, i = 1, 2$. Then the moment generating function of $Y = X_{1} \cdot X_{2}$ is

If G is a geometric mean of observations $x_{1}, x_{2}, \dots, x_{n}$ then the geometric mean of $y_{i} = e^{-\alpha \log_{e} x_{i}}$, $i = 1, 2, \dots, n$ is

In a set of 2n observations the geometric mean of first 'n' observations is 81 and the geometric mean of remaining n-observations is 16 then the geometric mean of all 2n observations is

You are given $P(A \cup B) = 0.6$ and $P(A \cup \overline{B}) = 0.8$ then $P(A)$ is

Consider $x_{1},x_{2},...,x_{n}$ observations such that $\sum_{i=1}^{n}{x_{i}}^{2}=500$ and $\sum_{i=1}^{n}x_{i}=50$. Then a minimum number of observations required is

If $P(E) = \frac{1}{3}$, $P(F) = \frac{2}{5}$ and $P(E \cup F) - P(E \cap F) = \frac{1}{5}$ then $P(E \cup F)$ is equal to

Which of the following statements are correct?
A. Ogive curves are used to obtain median

B. Histogram are used to obtain mode

C. Boxplots are used to determine mean

D. Pie charts are used to determine quantile

Choose the correct answer from the options given below

Let E, F and G be events such that $P(E|G) = 0.05$ and $P(F|G) = 0.05$ which of the following statement must be true?

Three dice have the probabilities of throwing a "five" as p, q and r respectively. One of the dice is chosen at random (each is equally likely to be chosen) and thrown and a "five" appeare
D. What is the probability that the die chosen was the first one?

Which of the following differential equation is satisfied by $y_{1}(x)=e^{x}$, $y_{2}(x)=x~e^{x}$ and $y_{3}=e^{2x}?$

The integrating factor for the differential equation $x~log_{e}x~dy = (2~log_{e}x - y) dx$ is

If $P(E)=\frac{1}{3}$, $P(F)=\frac{1}{5}$ and $P(E\cup F)=\frac{1}{2}$ then $P(E|\overline{F})+P(F|\overline{E})$ is equal to

If A and B are two non-mutually exclusive events such that $P(A|B)=P(B|A)$ then

Solution of differential equation $(x^{2}+y^{2})dx-2xy~dy=0,$ where c is constant, is

The eigen vectors of the matrix $A=\begin{bmatrix}5 & 4\\ 1& 2\end{bmatrix}$ is

If A is an invertible symmetric matrix then
A. $(A^{-1})^{T}=A^{-1}$

B. adj $A=(adj~A)^{T}$

C. $A^{-1}$ is skew-symmetric

D. $|A|=0$

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Let $AX=B$ be a system of n-linear equations in n unknowns then

If A and B are symmetric matrices of same order then
A. AB is symmetric iff $AB=BA$

B. $AB+BA$ is skew symmetric matrix

C. AB-BA is symmetric matrix

D. $(A+B)^{n}$ is symmetric for all $n \in N$

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Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals

The area of region in the first quadrant that is bounded by $y=\sqrt{x}$, $y=2-x$ and x-axis is

The value of $\lim_{x\rightarrow1}\frac{\int_{2 \log_{e}x}^{3\log_{e} x} e^{t} \, dt}{x-1}$ equals

The value of integral $\int_{0}^{1}\int_{x}^{1}\frac{1}{1+y^{2}}\cdot dydx$ is equal to