Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Given f(x) in a probability mass function
`sum_x` f(x) = 1
k2 + 2k2 + 3k2 + 2k + 3k = 1
6k2 + 5k = 1
6k2 + 5k – 1 = 0
(k + 1)(6k – 1) = 0
k = `1/6`
k ≠ –1 neglecting negative terms
Probability mass function
| x | 1 | 2 | 3 | 4 | 5 |
| F(x) | `1/36` | `2/36` | `3/36` | `2/6` | `3/6` |
APPEARS IN
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 and = 0 otherwise.
P (–0·5 < x or x > 0·5)
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)
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.
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).
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
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) = ?
Three fair coins are tossed simultaneously. Find the probability mass function for a number of heads that occurred
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 ≥ 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)
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:
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
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 ______
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) =
