ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 28 - 32 of 164

Let Z be a random variable with p. d. f. f (z) . Given that the quantile of z is defined as

X is a random variable with p. d. f. , then quantile is

Assume

Then the limit is

Lower limit is - and upper limit is

If z = then the integral is same for given z and the quantile is

So, the quantile of X is .

For balanced coin the probability is p = 0.5. For Bernoulli trails where n = 40,000, the mean and standard deviation is

Using Chebyshev՚s inequality,

The question says that the probability is at least 0.99 that is

So, the number of heads comes between is 19000 to 21000.

Hence, the probability is at least 0.99 that the proportion of heads will fall bet…

T he one-third rule of the integrand using Simpson՚s rule is

The area of the cross section of a river 80 feet wide is

Here n = 8, b = 80, a = 0, h = (b-a) /n = 10

we have known that is the sample variance of the sequence. The mean is

The convergence in probability is

Using Chebychev՚s inequality

Thus, sufficient condition is that convergence in probability to 1 is that .

E₁ = Box 1 2 white and 4 black when the fair dice value is x₁ = 1

E₂ = Box 2 4 white and 2 black when the fair dice value is x₂ = (2,3)

E₃ = Box 3 6 white when the fair dice value is x₃ = (4,5, 6)

X denotes the number of white balls out of randomly select 3 balls

Probability of selecting a ball in E₁ is

Similarly, Probability of selecting a ball in E₂ i…