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प्रश्न
Fill in the blank :
The value of continuous r.v. are generally obtained by _______
उत्तर
The value of continuous r.v. are generally obtained by Measurement.
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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)
The following is the p.d.f. of continuous r.v.
f (x) = `x/8`, for 0 < x < 4 and = 0 otherwise.
Find expression for c.d.f. of X
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).
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.
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.
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)
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, "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)
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:
The probability mass function of a random variable is defined as:
| x | – 2 | – 1 | 0 | 1 | 2 |
| f(x) | k | 2k | 3k | 4k | 5k |
Then E(X ) is equal to:
The p.m.f. of a random variable X is
P(x) = `(5 - x)/10`, x = 1, 2, 3, 4
= 0, otherwise
The value of E(X) is ______
If the c.d.f (cumulative distribution function) is given by F(x) = `(x - 25)/10`, then P(27 ≤ x ≤ 33) = ______.
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 ______
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) = ?
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.
