Advertisements
Advertisements
Question
c.d.f. of a discrete random variable X is
Options
an identity function
a step function
an even function
an odd function
Advertisements
Solution
a step function
APPEARS IN
RELATED QUESTIONS
Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.
`"f(x)" = {("k"(4 - x^2) "for –2 ≤ x ≤ 2,"),(0 "otherwise".):}`
P(–1 < x < 1)
The following is the p.d.f. of continuous r.v.
f (x) = `x/8` , for 0 < x < 4 and = 0 otherwise.
Find F(x) at x = 0·5 , 1.7 and 5
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)
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.
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."):}`
Verify whether f(x) is a p.d.f.
Fill in the blank :
The values of discrete r.v. are generally obtained by _______
Fill in the blank :
The value of continuous r.v. are generally obtained by _______
Solve the following problem :
Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.
Amount of syrup prescribed by a physician.
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.
A coin is tossed 10 times. The probability of getting exactly six heads is ______.
Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold 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 the cumulative distribution function
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 cumulative distribution function
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)
The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0, - oo < x < - 1),(0.15, - 1 ≤ x < 0),(0.35, 0 ≤ x < 1),(0.60, 1 ≤ x < 2),(0.85, 2 ≤ x < 3),(1, 3 ≤ x < oo):}`
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 P(2 ≤ X < 5)
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(X > 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:
A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is
Choose the correct alternative:
Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with Probability 0.5. Assume that the results of the flips are independent and let X equal the total number of heads that result. The value of E[X] is
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.
If A = {x ∈ R : x2 - 5 |x| + 6 = 0}, then n(A) = _____.
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.
| X = k | 0 | 1 | 2 | 3 | 4 |
| P(X = k) | 0.1 | 0.4 | 0.3 | 0.2 | 0 |
The variance of X is ______
Two coins are tossed. Then the probability distribution of number of tails is.
The c.d.f. of a discrete r.v. x is
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| F(x) | 0.16 | 0.41 | 0.56 | 0.70 | 0.91 | 1.00 |
Then P(1 < x ≤ 4) = ______
The p.d.f. of a continuous random variable X is
f(x) = 0.1 x, 0 < x < 5
= 0, otherwise
Then the value of P(X > 3) is ______
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.
At random variable X – B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are ______.
For the following distribution function F(x) of a rv.x.
| x | 1 | 2 | 3 | 4 | 5 | 6 |
| F(x) | 0.2 | 0.37 | 0.48 | 0.62 | 0.85 | 1 |
P(3 < x < 5) =
