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C.d.f. of a discrete random variable X is - Mathematics and Statistics

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प्रश्न

c.d.f. of a discrete random variable X is

विकल्प

  • an identity function

  • a step function

  • an even function

  • an odd function

MCQ

उत्तर

a step function

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Types of Random Variables
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2.7: Probability Distributions - MCQ

संबंधित प्रश्न

Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2 /3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P( x < –2)


Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2/ 3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P( X > 0)


Choose the correct option from the given alternative:

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

X 1 2 3 4 5 6 7
P(X=x) k 2k 2k 3k k2 2k2 7k2+k

k = 


In the p.m.f. of r.v. X

X 1 2 3 4 5
P (X) `1/20` `3/20` a 2a `1/20`

Find a and obtain c.d.f. of X. 


Solve the following problem :

A player tosses two coins. He wins ₹ 10 if 2 heads appear, ₹ 5 if 1 head appears, and ₹ 2 if no head appears. Find the expected value and variance of winning amount.


Solve the following problem :

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

A person on high protein diet is interested in the weight gained in a week.


Solve the following problem :

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

A highway safety group is interested in the speed (km/hrs) of a car at a check point.


The probability distribution of a r.v. X is

X = x -3 -2 -1 0 1
P(X = x) 0.3 0.2 0.25 0.1 0.15

Then F (-1) = ?


A random variable X has the following probability distribution:

X = x 0 1 2 3
P (X = x) `1/10` `1/2` `1/5` k

Then the value of k is


A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find P(4 ≤ X < 10)


A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find P(X ≥ 6)


Find the probability mass function and cumulative distribution function of a number of girl children in families with 4 children, assuming equal probabilities for boys and girls


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 the value of k


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)


A random variable X has the following probability mass function.

x 1 2 3 4 5
F(x) k2 2k2 3k2 2k 3k

Find the value of k


A random variable X has the following probability mass function.

x 1 2 3 4 5
F(x) k2 2k2 3k2 2k 3k

Find P(2 ≤ X < 5)


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:

Suppose that X takes on one of the values 0, 1 and 2. If for some constant k, P(X = i) = kP(X = i – 1) for i = 1, 2 and P(X = 0) = `1/7`. Then the value of k is


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.


A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is ______.


If the c.d.f (cumulative distribution function) is given by F(x) = `(x - 25)/10`, then P(27 ≤ x ≤ 33) = ______.


If A = {x ∈ R : x2 - 5 |x| + 6 = 0}, then n(A) = _____.


If the probability function of a random variable X is defined by P(X = k) = a`((k + 1)/2^k)` for k - 0, 1, 2, 3, 4, 5, then the probability that X takes a prime value is ______


For a random variable X, if Var (X) = 5 and E (X2) = 21, the value of E (X) is ______


A random variable X has the following probability distribution:

X 1 2 3 4
P(X) `1/3` `2/9` `1/3` `1/9`

1hen, the mean of this distribution is ______ 


X is a continuous random variable with a probability density function

f(x) = `{{:(x^2/4 + k;     0 ≤ x ≤ 2),(0;              "otherwise"):}`

The value of k is equal to ______


The probability distribution of a random variable X is given below. If its mean is 4.2, then the values of a and bar respectively 

X = x 1 2 3 4 5 6
P(X = x) a a a b b 0.3

The probability distribution of a random variable X is given below.

X = k 0 1 2 3 4
P(X = k) 0.1 0.4 0.3 0.2 0

The variance of X is ______


A card is chosen from a well-shuffled pack of cards. The probability of getting an ace of spade or a jack of diamond is ______.


The c.d.f. of a discrete r.v. X is

X = x -4 -2 -1 0 2 4 6 8
F(x) 0.2 0.4 0.55 0.6 0.75 0.80 0.95 1

Then P(X ≤ 4|X > -1) = ?


A random variable X has the following probability distribution:

X = xi 1 2 3 4
P(X = xi) 0.2 0.15 0.3 0.35

The mean and the variance are respectively ______.


Two cards are randomly drawn, with replacement. from a well shuffled deck of 52 playing cards. Find the probability distribution of the number of aces drawn.


If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to ______.


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