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QUESTION: 1

The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.

Que : The probability that more than 3 cars will arrive during any 10 min period is

Solution:

QUESTION: 2

The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.

Que: The probability that no car will arrive is

Solution:

QUESTION: 3

The power reflected from an aircraft of complicated shape that is received by a radar can be described by an exponential random variable W. The density of W is

where W_{0} is the average amount of received power. The probability that the received power is larger than the power received on the average is

Solution:

QUESTION: 4

Delhi averages three murder per week and their occurrences follow a poission distribution

Que: The probability that there will be five or more murder in a given week is

Solution:

QUESTION: 5

Delhi averages three murder per week and their occurrences follow a poission distribution

Que: On the average, how many weeks a year can Delhi expect to have no murders ?

Solution:

average number of week, per year with no murder

QUESTION: 6

Delhi averages three murder per week and their occurrences follow a poission distribution.

Que:How many weeds per year (average) can the Delhi expect the number of murders per week to equal orexceed the average number per week ?

Solution:

Average number of weeks per year that number of murder exceeds the average

QUESTION: 7

A discrete random variable X has possible values x_{ i} = i^{2} i =1, 2, 3, 4 which occur with probabilities 0.4, 0.25, 0.15, 0.1,. The mean value

Solution:

QUESTION: 8

The random variable X is defined by the density

The expected value of g(X) = X^{3} is

Solution:

QUESTION: 9

The random variables X and Y have variances 0.2 and 0.5 respectively. Let Z= 5X-2Y. The variance of Z is?

Solution:

Var(X) = 0.2, Var(Y) = 0.5

Z = 5X – 2Y

Var(Z) = Var(5X-2Y)

= Var(5X) + Var(2Y)

= 25Var(X) + 4Var(Y)

Var(Z) = 7.

QUESTION: 10

The variance of random variable X is

Solution:

Solution=

Variance of X is σ_{x}^{2}=E[X^{2}]- μ_{x}^{2}

E(X^{2})=_{-∞}^{∞} x2fx(x)dx=_{0}^{1} _{ }x^{2}(x)3(1-x)^{2}dx=1/10

σ_{x}^{2 }=(1/10)-(1/4)^{2}=3/80

hence option B would be the correct answer.

QUESTION: 11

A Random variable X is uniformly distributed on the interval (-5, 15). Another random variableY = e ^{-X/5 }is formed. The value of E[Y ] is

Solution:

QUESTION: 12

A joint sample space for two random variable X and Y has four elements (1, 1), (2, 2), (3, 3) and (4, 4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively.

Que: The probability of the event {X ≤ 2.5, Y ≤ 6} is

Solution:

QUESTION: 13

A joint sample space for two random variable X and Y has four elements (1, 1), (2, 2), (3, 3) and (4, 4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively.

Que: The probability of the event {X ≤ 3} is

Solution:

= 0.1+ 0.35 + 0.05 = 0.5

QUESTION: 14

The statistically independent random variable X and Y have mean values .and They have second moments and Consider a random variable W = 3X - Y.

Que: The mean value E [W] is

Solution:

QUESTION: 15

The statistically independent random variable X and Y have mean values .and They have second moments and Consider a random variable W = 3X - Y.

Que: The second moment of W is

Solution:

QUESTION: 16

The statistically independent random variable X and Y have mean values .and They have second moments and Consider a random variable W = 3X - Y.

Que: The variance of the random variable is

Solution:

QUESTION: 17

Two random variable X and Y have the density function

The X and Y are

Solution:

QUESTION: 18

The value of σ_{x}^{2} , σ_{y}^{2} , R_{XY} and ρ are respectively

Solution:

QUESTION: 19

The mean value of the random variable

W = (X + 3Y)^{2} + 2X + 3 is

Solution:

QUESTION: 20

If machine is not properly adjusted, the product resistance change to the case where a_{x }= 1050Ω. Now the rejected fraction is

Solution:

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