Recent questions tagged goclasses-da-dpp

Suppose $X \sim \operatorname{Normal}(\mu, 9)$. For $n=100$ iid samples of $X$, the observed sample mean is 11.8 . What conclusion would a z-test reach if the null hypoth...

The average marks scored by students of a school in their board exams is reported to be 400 with a standard deviation of 5 . You suspect that the average may be lower, po...

An urn contains $5$ white balls and $5$ red balls. $2$ balls are selected at random. Let $X$ denote the number of red balls drawn and let $Y$ denote the number of white b...

The joint probability mass function of three discrete random variables $X, Y$ and $Z$ is given as$$p(0,1,2)=p(0,2,3)=p(1,0,-2)=\frac{1}{3}$$Calculate $\operatorname{Var}(...

Let $X$ and $Y$ be two independent discrete random variables. Define random variables $U$ and $V$ as$$U=\frac{X-E(X)}{S D(X)}, \quad V=\frac{Y-E(Y)}{S D(Y)}$$Find $\opera...

Let the two random variables $X$ and $Y$ be independent with means equal to 10 and 20 , and variances equal to $2$ and $4$, respectively. Find the value of $\operatorname...

Suppose $1$ in $100$ products that are coming out of a production line is defective. Suppose we randomly pick and keep aside products from the production line till the fi...

If $X \sim \operatorname{Binomial}(n, p)$, then which of the following statements $/ \mathrm{s}$ is/are always true? ( $n>0$ and $0<p<1$ )$E(X) \leq \operatorname{Var}(X)...

Suppose that $X$ is a random variable for which $E(X)=m$ and $\operatorname{Var}(X)=v$. Find the positive values of $a$ and $b$ such that $Y=a X-b$, has expectation $0$ a...

Murad wants to open his door with $5$ keys (out of which $1$ will open the door) and tries the keys independently and at random. If unsuccessful keys are eliminated from ...

Amandeep is in the middle of a bridge of infinite length. He takes the unit step to the right with probability $p$ and to the left with probability $1-p$. Assume that the...

Amandeep is in the middle of a bridge of infinite length. He takes the unit step to the right with probability $p$ and to the left with probability $1-p$. Assume that the...

An unbiased die is thrown $n+2$ times. After each throw a ' + ' is recorded for 2 or 5 and '-' is recorded for $1,3,4$ or 6 , the signs forming an ordered sequence. To ea...

An unbiased die is thrown $n+2$ times. After each throw a ' + ' is recorded for 2 or 5 and '-' is recorded for $1,3,4$ or 6 , the signs forming an ordered sequence. To ea...

There are $2^{10}$ numbered cards in a deck among which ${ }^{10} C_{i}$ cards bear the number i ; $\mathrm{i}=0,1,2, \ldots, 10$. From the deck, 4 cards are drawn with r...

A and B predicts the outcomes of a cricket match and their chances of predicting the runs scored by a specific batsman correctly are $\frac{a}{b}$ and $\frac{c}{d}$ respe...

The phone brands OnePlus, Vivo and Oppo are owned by BBK Electronics. The table below represents the data for the sales (in Lakhs) of OnePlus and BBK Electronics by diffe...

The phone brands OnePlus, Vivo and Oppo are owned by BBK Electronics. The table below represents the data for the sales (in Lakhs) of OnePlus and BBK Electronics by diffe...

A stem-and-leaf plot below shows the ratings (out of 100) of an actor's performance in ten different movies.What is the new median rating, if 5 points are added to all of...

A stem-and-leaf plot below shows the ratings (out of 100) of an actor's performance in ten different movies.Stem-and-Leaf Plot of Actor's Ratings (Key: 5 / 3 represents a...

The sample variance of the retail prices (in rupees) of a certain commodity in a city was found to be $36$. Due to a change in tax policy, every retail price was first in...

In a dataset, the numbers $\mathbf{- 1}$ and $\mathbf{1}$ occur with frequencies of $(x-3)$ and $x$, respectively. The constraints of the data collection require that $x$...

In a deck, there are cards numbered $1$ to $n$ such that the number of cards of a given number is the same as the number on the card. Which of the following statement(s) ...

In a dataset, four numbers denoted as $a, b, c$, and $d$ appear with frequencies of ( $x+ 6),(x+2),(x-3)$, and $x$, respectively. The arithmetic mean of the dataset is $m...

The education minister wants to know the status of campus placements of B.Tech students in different engineering institutes of India. An analyst did a survey on the rando...

Suppose we build a neural network for a 5-class classification task. Suppose for a single training example, the true label is $\left[\begin{array}{lllll}1 & 0 & 0 & 0 & 0...

Consider a neural network with the number of neurons in different layers as mentioned in the below list for a regression task. The first layer is the input layer and the ...

Consider a neural network with the number of neurons in different layers as mentioned in the below list for a regression task. The first layer is the input layer and the ...

Consider a neural network with the number of neurons in different layers as mentioned in the below list for a regression task. The first layer is the input layer and the ...

Consider the following data:\[\begin{array}{|l|l|}\hlineg(x) & y \\\hline+30 & +1 \\\hline-20 & -1 \\\hline-1 & -1 \\\hline+1 & +1 \\\hline\end{array}\]Which of the follo...