Probability and Statistics MCQs Question and Answer in Engineering Maths

51

An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is

A) 0.067 B) 0.073 C) 0.082 D) 0.091

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Answer & Solution

Answer: Option C

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52

The standard deviation of a uniformly distributed random variable between 0 and 1 is

A) $$\frac{1}{{\sqrt {12} }}$$ B) $$\frac{1}{{\sqrt 3 }}$$ C) $$\frac{5}{{\sqrt {12} }}$$ D) $$\frac{7}{{\sqrt {12} }}$$

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Answer: Option A

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53

X and Y are two random independent events. It is known that P(X) = 0.40 and $${\text{P}}\left( {{\text{X}} \cup {{\text{Y}}^{\text{C}}}} \right) = 0.7.$$ Which one of the following is the value of $${\text{P}}\left( {{\text{X}} \cup {\text{Y}}} \right)\,?$$

A) 0.7 B) 0.5 C) 0.4 D) 0.3

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Answer: Option A

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54

A screening test is carried out to detect a certain disease. It is found that 12% of the positive reports and 15% of the negative reports are incorrect. Assuming that the probability of a person getting a positive report is 0.01, the probability that a person tested gets in incorrect report is

A) 0.0027 B) 0.0173 C) 0.1497 D) 0.2100

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Answer: Option C

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55

Suppose afair six-sided die is rolled once. If the value on the die is 1, 2 or 3 the die is rolled a second time. What is the probability that the sum of total values that turn up is at least 6?

A) $$\frac{{10}}{{21}}$$ B) $$\frac{5}{{12}}$$ C) $$\frac{2}{3}$$ D) $$\frac{1}{6}$$

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Answer & Solution

Answer: Option B

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56

If X is a discrete random variable that follows Binomial distribution, then which one of the following response relations is correct?

A) $${\text{P}}\left( {{\text{r}} + 1} \right) = \frac{{{\text{n}} - {\text{r}}}}{{{\text{r}} + 1}}{\text{P}}\left( {\text{r}} \right)$$ B) $${\text{P}}\left( {{\text{r}} + 1} \right) = \frac{{\text{p}}}{{\text{q}}}{\text{P}}\left( {\text{r}} \right)$$ C) $${\text{P}}\left( {{\text{r}} + 1} \right) = \frac{{{\text{n}} + {\text{r}}}}{{{\text{r}} + 1}}\frac{{\text{p}}}{{\text{q}}}{\text{P}}\left( {\text{r}} \right)$$ D) $${\text{P}}\left( {{\text{r}} + 1} \right) = \frac{{{\text{n}} - {\text{r}}}}{{{\text{r}} + 1}}\frac{{\text{p}}}{{\text{q}}}{\text{P}}\left( {\text{r}} \right)$$

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Answer & Solution

Answer: Option D

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57

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

A) 2 and 2 B) 1 and 2 C) 2 and 1 D) 1 and 1

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Answer: Option B

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58

If the difference between the expectation of the square of a random variable (E[x²]) and the square of the expectation of the random variable (E[x])² is denoted by R, then

A) R = 0 B) R < 0 C) R ≥ 0 D) R > 0

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Answer & Solution

Answer: Option C

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59

The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is

A) y - x B) $$\frac{1}{{{\text{y}} - {\text{x}}}}$$ C) x - y D) $$\frac{1}{{{\text{x}} - {\text{y}}}}$$

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Answer & Solution

Answer: Option B

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60

If P(x) = $$\frac{1}{4}$$, P(Y) = $$\frac{1}{3}$$ and $${\text{P}}\left( {{\text{X}} \cap {\text{Y}}} \right) = \frac{1}{{12}},$$ the value of $${\text{P}}\left( {\frac{{\text{Y}}}{{\text{X}}}} \right)$$ is

A) $$\frac{1}{4}$$ B) $$\frac{4}{{25}}$$ C) $$\frac{1}{3}$$ D) $$\frac{{29}}{{50}}$$

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Answer & Solution

Answer: Option C

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