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[#56] The function p(x) is given by $${ ext{p}}left( { ext{x}}
ight) = frac{{ ext{A}}}{{{{ ext{x}}^mu }}}$$ xa0 where A and μ are constants with μ > 1 and 1 ≤ x < $$infty $$ and p(x) = 0 for $$ - infty $$ xa0< x < 1. For p(x) to be a probability density function, the value of A should be equal to

(A) μ - 1

(B) μ + 1

(C) $$frac{1}{{left( {mu - 1} ight)}}$$

(D) $$frac{1}{{left( {mu + 1} ight)}}$$

Correct Answer

(A) μ - 1

[#57] A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?

(A) $${left( {frac{1}{2}} ight)^2}$$

(B) $${}^{10}{{ ext{C}}_2}{left( {frac{1}{2}} ight)^2}$$

(C) $${left( {frac{1}{2}} ight)^{10}}$$

(D) $${}^{10}{{ ext{C}}_2}{left( {frac{1}{2}} ight)^{10}}$$

Correct Answer

(C) $${left( {frac{1}{2}} ight)^{10}}$$

[#58] The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is

(A) 0.029

(B) 0.034

(C) 0.039

(D) 0.044

Correct Answer

(B) 0.034

[#59] 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 p 2 is

(A) $$frac{2}{3}$$

(B) 1

(C) $$frac{4}{3}$$

(D) $$frac{5}{3}$$

Correct Answer

(D) $$frac{5}{3}$$

[#60] 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

(A) √μ

(B) μ 2

(C) μ

(D) $$frac{1}{mu }$$

Correct Answer

(A) √μ