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(X ≥ 6)
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(X ≥ 6) = P(X = 6) + P(X = 8) + P(X = 10)
= `10/36 + 12/36 + 9/36`
= `31/36`
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 and = 0 otherwise.
P (–0·5 < x or x > 0·5)
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
The following is the p.d.f. of continuous r.v.
f (x) = `x/8` , for 0 < x < 4 and = 0 otherwise.
Find F(x) at x = 0·5 , 1.7 and 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 < 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)
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.
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.
F(x) is c.d.f. of discrete r.v. X whose p.m.f. is given by P(x) = `"k"^4C_x` , for x = 0, 1, 2, 3, 4 and P(x) = 0 otherwise then F(5) = _______
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.
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.
A person on high protein diet is interested in the weight gained in a week.
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.
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) = ?
A coin is tossed 10 times. The probability of getting exactly six heads is ______.
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
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 P(X < 1)
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(2 ≤ X < 5)
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)
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) = ?
Let X = time (in minutes) that lapses between the ringing of the bell at the end of a lecture and the actual time when the professor ends the lecture. Suppose X has p.d.f.
f(x) = `{(kx^2"," 0 ≤ x ≤ 2), (0"," "othenwise"):}`
Then, the probability that the lecture ends within 1 minute of the bell ringing is ______
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 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 ______
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 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 ______
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 ______
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) = ______.
