HSC Arts Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find the value of k 

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find the distribution function

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(X < 3)

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(5 ≤ X)

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(X ≤ 4)

If X is the random variable with probability density function f(x) given by,
`f(x) = {{:(x + 1",", -1 ≤ x < 0),(-x +1",",   0 ≤ x < 1),(0, "otherwise"):}`
then find the distribution function F(x)

If X is the random variable with probability density function f(x) given by,
`f(x) = {{:(x + 1",", -1 ≤ x < 0),(-x +1",",   0 ≤ x < 1),(0, "otherwise"):}`
then find P(– 0.5 ≤ x ≤ 0.5)

If X is the random variable with distribution function F(x) given by,
F(x) = `{{:(0",", - oo < x < 0),(1/2(x^2 + x)",", 0 ≤ x ≤ 1),(1",", 1 ≤ x < oo):}`
then find the probability density function f(x)

If X is the random variable with distribution function F(x) given by,
F(x) = `{{:(0",", - oo < x < 0),(1/2(x^2 + x)",", 0 ≤ x ≤ 1),(1",", 1 ≤ x < oo):}`
then find P(0.3 ≤ X ≤ 0.6)

Choose the correct alternative:

Let X be random variable with probability density function
`f(x) = {(2/x^3, x ≥ 1),(0, x < 1):}`
Which of the following statement is correct?

Choose the correct alternative:

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is 
`f(x) = {{:(1/l, 0 < x < l),(0, l ≤ x < 2l):}`
The mean and variance of the shorter of the two pieces are respectively

Choose the correct alternative:

If the function f(x) = `1/12` for a < x < b, represents a probability density function of a continuous random variable X, then which of the following cannot be the value of a and b?

Choose the correct alternative:

The random variable X has the probability density function
`f(x) = {{:("a"x + "b", 0 < x < 1),(0, "otherwise"):}`
and E(X) = `7/12`, then a and b are respectively

Choose the correct alternative:

If `f(x) = {{:(2x, 0 ≤ x ≤ "a"),(0, "otherwise"):}` is a probability density function of a random variable, then the value of a is

Choose the correct alternative:

A computer salesperson knows from his past experience that he sells computers to one in every twenty customers who enter the showroom. What is the probability that he will sell a computer to exactly two of the next three customers?

If the direction cosines of a line are `(1/c, 1/c, 1/c)` then ______.

If z = (ax + b) (cy + d), then find `(∂z)/(∂x)` and `(∂z)/(∂y)`.

Test for consistency and if possible, solve the following systems of equations by rank method:

x – y + 2z = 2, 2x + y + 4z = 7, 4x – y + z = 4

Test for consistency and if possible, solve the following systems of equations by rank method:

3x + y + z = 2, x – 3y + 2z = 1, 7x – y + 4z = 5

Test for consistency and if possible, solve the following systems of equations by rank method:

2x + 2y + z = 5, x – y + z = 1, 3x + y + 2z = 4