A year is chosen at random from the set of years {2012, 2013, … , 2021}. From the chosen year, a month is chosen at random and from the chosen month, a day is chosen at random. Given that the chosen day is the 29 th of a month, the conditional probability that the chosen month is February equals

The correct option is (A) : \(\frac{279}{9965}\) .

A year is chosen at random from the set of years {2012,2013,..,2021}.From the chosen year,a month is chosen at random and from the chosen month,a day is chosen

Suppose that the weights (in kgs) of six months old babies, monitored at a healthcare facility, have

N(\mu, \sigma^2)

distribution, where

\mu \in \mathbb{R}

and

\sigma > 0

are unknown parameters. Let

X_1, X_2, \ldots, X_9

be a random sample of the weights of such babies. Let

\overline{X} = \frac{1}{9} \sum_{i=1}^{9} X_i

,

S = \sqrt{\frac{1}{8} \sum_{i=1}^{9} (X_i - \overline{X})^2}

and let a 95% confidence interval for

\mu

based on

t

-distribution be of the form

(\overline{X} - h(S), \overline{X} + h(S))

, for an appropriate function

h

of random variable

S

. If the observed values of

\overline{X}

and

S^2

are 9 and 9.5, respectively, then the width of the confidence interval is equal to __________ (round off to 2 decimal places) (You may use

t_{9,0.025} = 2.262, t_{8,0.025} = 2.306, t_{9,0.05} = 1.833, t_{8,0.05} = 1.86

).

IIT JAM MS - 2024
Multivariate Distributions

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Let

X_1, X_2, X_3

be a random sample from a Poisson distribution with mean

\lambda

,

\lambda > 0

. For testing

H_0: \lambda = \frac{1}{8}

against

H_1: \lambda = 1

, a test rejects

H_0

if and only if

X_1 + X_2 + X_3 > 1

. The power of this test is equal to __________ (round off to 2 decimal places).

IIT JAM MS - 2024
Standard Univariate Distributions

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Let

\Theta

be a random variable having

U(0, 2\pi)

distribution. Let

X = \cos \Theta

and

Y = \sin \Theta

. Let

\rho

be the correlation coefficient between

X

and

Y

. Then

100\rho

is equal to __________ (answer in integer).

IIT JAM MS - 2024
Univariate Distributions

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Consider a coin for which the probability of obtaining head in a single toss is

\frac{1}{3}

. Sunita tosses the coin once. If head appears, she receives a random amount of

X

rupees, where

X

has the

\text{Exp}\left( \frac{1}{9} \right)

distribution. If tail appears, she loses a random amount of

Y

rupees, where

Y

has the

\text{Exp}\left( \frac{1}{3} \right)

distribution. Her expected gain (in rupees) is equal to __________ (answer in integer).

IIT JAM MS - 2024
Probability

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Let

X

be a discrete random variable with

P(X \in \{-5, -3, 0, 3, 5\}) = 1

. Suppose that

P(X = -3) = P(X = -5)

,

P(X = 3) = P(X = 5)

and

P(X > 0) = P(X = 0) = P(X < 0)

. Then the value of

12P(X = 3)

is equal to __________ (answer in integer).

IIT JAM MS - 2024
Multivariate Distributions

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A year is chosen at random from the set of years {2012, 2013, … , 2021}. From the chosen year, a month is chosen at random and from the chosen month, a day is chosen at random. Given that the chosen day is the 29^th of a month, the conditional probability that the chosen month is February equals

The Correct Option is A

Solution and Explanation

Top Questions on Estimation

Questions Asked in IIT JAM MS exam

A year is chosen at random from the set of years {2012, 2013, … , 2021}. From the chosen year, a month is chosen at random and from the chosen month, a day is chosen at random. Given that the chosen day is the 29th of a month, the conditional probability that the chosen month is February equals

The Correct Option is A

Solution and Explanation

Top Questions on Estimation

Questions Asked in IIT JAM MS exam

A year is chosen at random from the set of years {2012, 2013, … , 2021}. From the chosen year, a month is chosen at random and from the chosen month, a day is chosen at random. Given that the chosen day is the 29^th of a month, the conditional probability that the chosen month is February equals