Recent questions and answers in Probability and Statistics

1
If the values of two random variables $(X,Y)$ are $(121, 360)$, $(242, 364)$ and $(363, 362)$, the value of correlation coefficient between $X$ and $Y$ (rounded off to one decimal place) is ________.
2
The median value for the dataset $\left ( 12, 10,16,8,90,50,30,24 \right )$ is ______________.
3
A normal random variable has mean equal to $0$, and standard deviation equal to $3$. The probability that on a random draw the value of this random variable is greater than $0$ is __________ (round off to $2$ decimal places).
4
Runs scored by a batsman in five one-day matches are $55$, $75$, $67$, $88$ and $15$. The standard deviation is _________
5
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________
6
For a discrete random variable $X$, $\textit{ran}(X)=\{0,1,2,3\}$ and the cumulative probability $F(X )$ is shown below: $\begin{array}{|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 \\ \hline F(X) & 0.5 & 0.6 & 0.8 & 1.0 \\ \hline \end{array}$The mean value of $X$ is ___________
7
If an unbiased coin is tossed $10$ times, the probability that all outcomes are same will be_______ $\times 10^{-5}$
8
Consider the data set $14, 18, 14, 14, 10, 29, 33, 31, 25$. If you add $20$ to each of the values, then both mean and variance change both mean and variance are unchanged the mean is unchanged, variance changes the mean changes, the variance is unchanged
9
A disease is inherited by a child with a probability of $1/4$. In a family with two children, the probability that exactly one sibling is affected by this disease is $1/4$ $3/8$ $7/16$ $9/16$
10
The probability distribution for a discrete random variable $X$ is given below. $\begin{array}{|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 \\ \hline P(X) & 0.3 & 0.4 & 0.2 & 0.1 \\ \hline \end{array}$The expectation value of $X$ is (up to one decimal place) _____________
The variable $z$ has a standard normal distribution. If $P(0 \leq z \leq 1)= 0.34$ then $P(z^2 > 1)$ is equal to (up to two decimal places) ____________
Consider an unfair coin. The probability of getting heads is $0.6$. If you toss this coin twice, what is the probability that the fast or the second toss is heads? $0.56$ $0.64$ $0.84$ $0.96$