Advertisements
Advertisements
Question
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)
Advertisements
Solution
Let X be the random variable denotes the total score in two thrown of a die.
Sample space S
| I\II | 1 | 3 | 3 | 5 | 5 | 5 |
| 1 | 2 | 4 | 4 | 6 | 6 | 6 |
| 3 | 4 | 6 | 6 | 8 | 8 | 8 |
| 3 | 4 | 6 | 6 | 8 | 8 | 8 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
n(S) = 36
X = {2, 4, 6, 8, 10}
| Values of the random variable | 2 | 4 | 6 | 8 | 10 | Total |
| Number of elements in inverse image | 1 | 4 | 10 | 12 | 9 | 36 |
Cumulative distribution function
P(4 ≤ X < 10) = P(X = 4) + P(X = 6) + P(X = 8)
= `4/36 + 10/36 + 12/36`
= `26/36`
= `13/18`
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 and = 0 otherwise.
P(x > 0)
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)
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( X > 0)
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 probability that X is between 1 and 3..
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.
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) = ?
A random variable X has the following probability distribution:
| X = x | 0 | 1 | 2 | 3 |
| P (X = x) | `1/10` | `1/2` | `1/5` | k |
Then the value of k is
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 the value of k
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
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 < 3)
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 ______
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 ______.
Two coins are tossed. Then the probability distribution of number of tails is.
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 ______
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 ______.
If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to ______.
