Recent questions tagged probability

GATE 2018 | MATHS | QI47
Let $\{X_i\}$ be a sequence of independent Poisson($\lambda$) variables, and let $W_n = \frac{1}{n} \sum_{i=1}^{n} X_i$. Then the limiting distribution of $\sqrt{n}(W_n - \lambda)$ is the normal distribution with zero mean and variance given by (A) $1$ (B) $\sqrt{\lambda}$ (C) $\lambda$ (D) $\frac{\lambda}{2}$

Let $\{X_i\}$ be a sequence of independent Poisson($\lambda$) variables, and let $W_n = \frac{1}{n} \sum_{i=1}^{n} X_i$. Then the limiting distribution of \(\sqrt{n...

rajveer43

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rajveer43 asked Jan 11

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GATE 2018 | MATHS | QUESTION 34
Let the cumulative distribution function of the random variable $X$ be given by \[ F_X(x) = \begin{cases} 0 & \text{if } x < 0 \\ x & \text{if } 0 \leq x < \frac{1}{2} \\ \frac{1 + x}{2} & \text{if } \frac{1}{2} \leq x < 1 \\ 1 & \text{if } x \geq 1 \end{cases} \] Then, the probability $P(X = \frac{1}{2})$ is given by

Let the cumulative distribution function of the random variable $X$ be given by\[ F_X(x) = \begin{cases} 0 & \text{if } x < 0 \\x & \text{if } 0 \leq x < \frac{1}{2} \\...

rajveer43

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rajveer43 asked Jan 11

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1 answer

GATE 2018 | MATHS | Q-33
Let $X$ and $Y$ have a joint probability density function given by \[ f_{X,Y}(x, y) = \begin{cases} 2 & \text{if } 0 \leq x \leq 1 - y \text{ and } 0 \leq y \leq 1 \\ 0 & \text{otherwise} \end{cases} \] If $f_Y$ denotes the marginal probability density function of $Y$, then $f_Y(1/2)$ is given by

Let $X$ and $Y$ have a joint probability density function given by\[ f_{X,Y}(x, y) = \begin{cases} 2 & \text{if } 0 \leq x \leq 1 - y \text{ and } 0 \leq y \leq 1 \\0...

rajveer43

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rajveer43 asked Jan 11

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GATE 2022 | Statistics | GATE-DA Sample Question
A company sometimes stops payments of quarterly dividends. If the company pays the quarterly dividend, the probability that the next one will be paid is $0.7$. If the company stops the quarterly dividend, the probability that the next ... (rounded off to three decimal places) that the company will not pay quarterly dividend in the long run is ______.

A company sometimes stops payments of quarterly dividends. If the company pays the quarterly dividend, the probability that the next one will be paid is $0.7$. If the com...

rajveer43

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rajveer43 asked Jan 10

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GATE Practice Problem | Probability
Two defective bulbs are present in a set of five bulbs. To remove the two defective bulbs, the bulbs are chosen randomly one by one and tested. If $𝑋$ denotes the minimum number of bulbs that must be tested to find out the two defective bulbs, then $𝑃(𝑋 = 3)$ (rounded off to two decimal places) equals _______________

Two defective bulbs are present in a set of five bulbs. To remove the two defective bulbs, the bulbs are chosen randomly one by one and tested. If $𝑋$ denotes the mini...

rajveer43

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rajveer43 asked Jan 10

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GATE DA Paper | Practice Problems
Let $𝑌_1 < 𝑌_2 < ⋯ < 𝑌_n$ be the order statistics of a random sample of size $𝑛$ from a continuous distribution, which is symmetric about its mean $𝜇$. Then the smallest value of $𝑛$ (in integer) such that $𝑃(𝑌1 < 𝜇 < 𝑌) ≥ 0.99$, is ______.

Let $𝑌_1 < 𝑌_2 < ⋯ < 𝑌_n$ be the order statistics of a random sample of size $𝑛$ from a continuous distribution, which is symmetric about its mean $𝜇$. T...

rajveer43

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rajveer43 asked Jan 10

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GATE 2021 | Statistics | Q-3

rajveer43

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rajveer43 asked Jan 10

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1 answer

GATE 2022 | Statistics | Q- 57
In a laboratory experiment, the behavior of cats are studied for a particular food preference between two foods $A$ and $B$ . For an experiment, 70% of the cats that had food A will prefer food A, and 50% of the cats that had food ... experiment, then the percentage (rounded off to one decimal place) of cats those will prefer food A in the third experiment, is ______

In a laboratory experiment, the behavior of cats are studied for a particular food preference between two foods $A$ and $B$ . For an experiment, 70% of the cats that had ...

rajveer43

129 views

rajveer43 asked Jan 10

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GATE Statistics Question 34

rajveer43

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rajveer43 asked Jan 9

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GATE CS Probabilty 2022 statistics paper

rajveer43

57 views

rajveer43 asked Jan 9

2 votes

1 answer

probability
8 pairs of hand gloves are on a shelf ( each of different colour). Four gloves are selected at random, the probability that there will be at least one pair is?

8 pairs of hand gloves are on a shelf ( each of different colour). Four gloves are selected at random, the probability that there will be at least one pair is?

practicalmetal

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practicalmetal asked Jan 3

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#self doubt
Telephone calls arrive at an exchange according to the Poisson process at a rate λ= 2/min. Calculate the probability that exactly two calls will be received during each of the first 5 minutes of the hour. the given solution is: Assume that N is the number of calls received during 1 ... 5) = 32 x e-10 P(M =5) = 0.00145, where e is a constant, which is approximately equal to 2.718.

Telephone calls arrive at an exchange according to the Poisson process at a rate λ= 2/min. Calculate the probability that exactly two calls will be received during each ...

Dknights

536 views

Dknights asked Dec 29, 2023

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4 answers

Made Easy Probability - Let X be a set containing n elements. Three subsets A,B, C of X are chosen at random. The probability that A, B, C are pairwise disjoint is? (What do they mean by pairwise disjoint? and how should I approach this question?)

tishhaagrawal

1.1k views

tishhaagrawal asked Dec 4, 2023

1 votes

1 answer

Made Est Test Series : How to find the expected number of dice rolls required to get 2 consecutive sixes? Can someone please explain an easy way to tackle such questions.

tishhaagrawal

519 views

tishhaagrawal asked Dec 4, 2023

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0 answers

Janko Gravner, Lecture Notes for Introductory Probability. Ex. 4.22
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails? For part a) ... ) + 20C12(12C2)(p/2)^10(1-p/2)^2 + ... + 20C20(20C10)(p/2)^10(1-p/2)^10

Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the fir...

ktushar

175 views

ktushar asked Nov 23, 2023

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