Probability-Standard Probability Distributions (ISS Statistics Paper I (Old Subjective Pattern)): Questions 8 - 12 of 22

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 165 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 550.00 or

Question number: 8

» Probability » Standard Probability Distributions » Uniform

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let X be a random variable with a continuous distribution function F. Show that F (X) has the uniform distribution on (0, 1).

Explanation

Let U = F (x), then the distribution function of G of U is given by

G(u)=P[Uu]=P[F(X)u]=P[XF1(u)]

The… (93 more words) …

Question number: 9

» Probability » Standard Probability Distributions » Cauchy

Appeared in Year: 2012

Essay Question▾

Describe in Detail

For the Cauchy distribution given by

f(x)=kσ2+(xμ)2,<x<

where k is a constant to be suitably chosen, derive the expression for the distribution function. Hence obtain a measure of central tendency and a measure of dispersion. What are the points of inflexion of the distribution?

Explanation

We choose k as constant that gives the integral over the range x for the density function is equal to one.

kσ2+(xμ)2dx=1

kσ[tan1(xμσ… (381 more words) …

Question number: 10

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2012

Essay Question▾

Describe in Detail

12.3 % of the candidates in a public examination score at least 70%, while another 6.3 % score at most 30%. Assuming the underlying distribution to be normal, estimate the percentage of candidates scoring 80 % or more.

Explanation

Let total marks obtain is 100. Assuming the underlying distribution to be normal, the mean µ and variance σ 2. It is given that

P(X70)=P(z70μσ2)=0.123

The value of z corresponding to… (173 more words) …

Question number: 11

» Probability » Standard Probability Distributions » Binomial

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let X 1, X 2, …, X m be i. i. d. random variables with common p. m. f.

P(X=k)=(nk)pk(1p)nk,k=0, 1,2,,n;0<p<1

obtain the p. m. f. of S m = X 1 + X 2 + …. + X m.

Explanation

Let X 1, X 2, …, X m i. i. d. random variables with common p. m. f. is P (X = k) which is a binomail random variables with common parameters n and p respectively. Then, the p. m. f. of S m = X 1 +… (263 more words) …

Question number: 12

» Probability » Standard Probability Distributions » Gamma

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let

f(x)=1Γnβnxn1exβ,x>0,n>0,β>0

Show that f (x) is a probability density function. Obtain V (X).

Explanation

if X is a continuous random variable and f (x) is a continuous function of X, then f (x) is a probability density function if

0f(x)dx=1

0f(x)dx=01… (380 more words) …

Sign In