Random Variables

Three fair coins are tossed simultaneously. Find the probability mass function for a number of heads that occurred

Fill in the blank :

The value of continuous r.v. are generally obtained by _______

Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by 
`f(x) = {{:((x^2 + 1)/k","  "for"  x = 0","  1","  2),(0","  "otherwise"):}` 
Find P(X ≥ 1)

Choose the correct alternative:

The probability mass function of a random variable is defined as:

Then E(X ) is equal to:

It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64),  "for"  0 ≤ x ≤ 4),(0,   "otherwise."):}`
Find probability that X is between 1 and 3..

The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0,  "for" - oo < x < 0),(1/2,  "for"  0 ≤ x < 1),(3/5,  "for"  1 ≤ x < 2),(4/5,  "for"  2 ≤ x < 4),(9/5,  "for"  3 ≤ x < 4),(1,  "for"   ≤ x < oo):}`
Find P(X ≥ 2)

Choose the correct alternative:

Which of the following is a discrete random variable?
I. The number of cars crossing a particular signal in a day.
II. The number of customers in a queue to buy train tickets at a moment.
III. The time taken to complete a telephone call.

Choose the correct option from the given alternative:

If the a d.r.v. X has the following probability distribution:

k =