Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
F(0) = P(x ≤ 0)
= P(x = 0)
= `1/8`
F(1) = P(x ≤ 1)
= P(x = 0) + P(x = 1)
= `1/8 + 2/8`
= `3/8`
F(2) = P(x ≤ 2)
= P(x = 0) + P(x = 1) + P(x = 2)
= `1/8 + 2/8 + 5/8`
= 1
| x | 0 | 1 | 2 |
| F(x) | `1/8` | `3/8` | 1 |
APPEARS IN
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 < 1)
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(1 < x < 2)
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 =
Solve the following :
Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.
An economist is interested the number of unemployed graduate in the town of population 1 lakh.
The p.m.f. of a r.v. X is given by P (X = x) =`("" ^5 C_x ) /2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise.
Then show that P (X ≤ 2) = P (X ≥ 3).
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.
An economist is interested in knowing the number of unemployed graduates in the town with a population of 1 lakh.
Solve the following problem :
Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.
Twelve of 20 white rats available for an experiment are male. A scientist randomly selects 5 rats and counts the number of female rats among them.
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.
c.d.f. of a discrete random variable X 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
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)
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 the probability mass function
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)
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 ≥ 2)
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
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 the probability mass function
If Xis a.r.v. with c.d.f F (x) and its probability distribution is given by
| X = x | - 1.5 | -0.5 | 0.5 | 1.5 | 2.5 |
| P(X = x) | 0.05 | 0.2 | 0.15 | 0.25 | 0.35 |
then, F(1.5) - F(- 0.5) = ?
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:
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 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 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 | 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 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) = ?
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.
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) =
