Engineering Maths · all questions

Probability and Statistics
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Q81

Open question

A point is randomly selected with uniform probability in the X-Y. plane within the rectangle with corners at (0, 0), (1, 0), (1, 2) and (0, 2). If P is the length of the position vector of the point, the expected value of p² is

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Q82

Open question

Let X₁, X₂ be two independent normal random variables with means μ₁, μ₂ and standard deviations σ₁, σ₂ respectively. Consider Y = X₁ - X₂; μ₁ = μ₂ = 1, σ₁ = 1, σ₂ = 2, Then,

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Q83

Open question

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is μ. The standard deviation for this distribution is given by

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Q84

Open question

Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) =

\frac{1}{2}

, the values of

P (\frac{A}{B})

and

P (\frac{B}{A})

respectively are

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Q85

Open question

An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is

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Q86

Open question

The probability of obtaining at least two "SIX" in throwing a fair dice 4 times is

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Q87

Open question

A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is

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Q88

Open question

Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

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Q89

Open question

The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is

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Q90

Open question

X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X - Y. The variance of Z is

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Q91

Open question

Let the probability density function of a random variable, X, be given as:

f_{x} (x) = \frac{3}{2} e^{- 3 x} u (x) + a e^{4 x} u (- x)

where u(x) is the unit step function. Then the value of 'a' and Prob{X ≤ 0}, respectively, are

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Q92

Open question

A random variable is uniformly distributed over the interval 2 to 10. Its variance will be

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Q93

Open question

A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is

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Q94

Open question

The value of the integral

I = \frac{1}{2 π} 0 \int \infty exp (- \frac{x ^{2}}{8}) dx

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Q95

Open question

The diameters of 10000 ball bearings were measured. The mean diameter and standard deviation were found to be 10 mm and 0.05 mm respectively. Assuming Gaussian distribution of measurements, it can be expected that the number of measurement more than 10.15 mm will be

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Q96

Open question

For the function f(x) = a + bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct?

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Q97

Open question

A continuous random variable X has a probability density f(x) = e^-x, 0 < x <

\infty

. Then P{X > 1} is

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Q98

Open question

Two white and two black balls, kept in two bins are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a white face picked?

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Q99

Open question

If a random variable X satisfies the Poisson's distribution with a mean value of 2, then probability that X ≥ 2 is

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Q100

Open question

If probability density function of a random variable x is
f(x) = x² for -1 ≤ x ≤ 1, and
= 0 for any other value of x
then, the percentage probability

P (- \frac{1}{3} ⩽ x ⩽ \frac{1}{3})

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Probability and Statisticspractice.

Probability and Statistics
practice.