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प्रश्न
c.d.f. of a discrete random variable X is
पर्याय
an identity function
a step function
an even function
an odd function
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उत्तर
a step function
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संबंधित प्रश्न
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)
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 and = 0 otherwise.
P (–0·5 < x or x > 0·5)
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).
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.
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 P(0 < X ≤ 1).
Fill in the blank :
The values of discrete 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.
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) = ?
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 ______.
Three fair coins are tossed simultaneously. Find the probability mass function for a number of heads that occurred
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 probability mass 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(4 ≤ X < 10)
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 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)
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 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 the probability mass function
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 < 3)
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) = ?
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 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 ______
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 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) = ?
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 ______
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.
A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) = ______.
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) =
