Recent activity in Probability and Statistics

Two fair six-sided dice, with sides numbered $1$ to $6$ , are thrown once. The probability of getting $7$ as the sum of the numbers on the top side of the dice is $\_\_\_...

The six faces of a cube (die) are numbered as $1,2,3,4,5$ and $6$, and it is rolled once. An outcome is the observed number on the top face. If the probability of getting...

Two fair six-sided dice are thrown. The probability of getting $12$ as the product of the numbers on the dice (rounded off to two decimal places) is __________.

The number of different possible ways of forming five intramolecular disulfide bonds with ten cysteine residues of a protein is ______________.

Ten playing cards numbered $1,2,3, \ldots, 10$ are placed face down on a table. One card is drawn at random, its number recorded, and then replaced face down. A card is d...

The probability density function of a random variable $X$ is $p(x) = 2e^{-2x}.$ The probability $P(1 \leq X \leq 2)$ (rounded off to two decimal places) is _________.

Consider a random variable $X$ with mean $\mu_{x}=0.1$ and variance $\sigma_{x}^{2}=0.2.$ A new random variable $Y=2X+1$ is defined. The variance of the random variable $...

Three balls, colored in blue, green and red, are successively transferred from box $A$ to box $B$ in the order $\text{BLUE-GREEN-RED.}$ The probability of a reverse trans...

An algorithm was designed to find globins in protein sequence databases. A database which has $78$ globin sequences was searched using this algorithm. The algorithm retri...

A new game is being introduced in a casino. A player can lose Rs. $100$, break even, win Rs. $100$, or win Rs. $500$. The probabilities $(P(X))$ of each of these outcomes...

The distribution of marks scored by a large class in an exam can be represented as a normal distribution with mean $\mu$ and standard deviation $\sigma$. In a follow-up e...

At the transcription start site of a gene, any of the four nucleotides can occur with equal probability $p$. The Shannon Entropy $S$, given by $S= – \Sigma_{i=1}^4 p_i \l...

A heterozygous tall plant $(Tt)$ was crossed with a homozygous dwarf plant $(tt)$. The resultant seeds were collected. If five seeds are chosen at random, then the probab...

One percent of the cars manufactured by a company are defective. What is the probability (upto four decimals) that more than two cars are defective, if $100$ cars are pro...

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 on...

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 th...

The median value for the dataset $\left ( 12, 10,16,8,90,50,30,24 \right )$ is ______________.

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) ____________

Standard error isthe probability of a type I error in a statistical testthe error in estimating a sample standard deviationthe standard deviation of a variable that follo...

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$$...

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...

For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________

Runs scored by a batsman in five one-day matches are $55$, $75$, $67$, $88$ and $15$. The standard deviation is _________

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 & ...

If an unbiased coin is tossed $10$ times, the probability that all outcomes are same will be_______ $ \times 10^{-5}$

Consider the data set $14, 18, 14, 14, 10, 29, 33, 31, 25$. If you add $20$ to each of the values, thenboth mean and variance changeboth mean and variance are unchangedth...

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$1/4$...