Advertisements
Advertisements
Question
Choose the correct alternative:
A variable that can assume any possible value between two points is called
Options
Discrete random variable
Continuous random variable
Discrete sample space
Random variable
Solution
Continuous random variable
APPEARS IN
RELATED QUESTIONS
Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images
Let X be a discrete random variable with the following p.m.f
`"P"(x) = {{:(0.3, "for" x = 3),(0.2, "for" x = 5),(0.3, "for" x = 8),(0.2, "for" x = 10),(0, "otherwise"):}`
Find and plot the c.d.f. of X.
The discrete random variable X has the probability function.
Value of X = x |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
If P(X ≤ x) > `1/2`, then find the minimum value of x.
The distribution of a continuous random variable X in range (– 3, 3) is given by p.d.f.
f(x) = `{{:(1/16(3 + x)^2",", - 3 ≤ x ≤ - 1),(1/16(6 - 2x^2)",", - 1 ≤ x ≤ 1),(1/16(3 - x)^2",", 1 ≤ x ≤ 3):}`
Verify that the area under the curve is unity.
Suppose that the time in minutes that a person has to wait at a certain station for a train is found to be a random phenomenon with a probability function specified by the distribution function
F(x) = `{{:(0",", "for" x ≤ 0),(x/2",", "for" 0 ≤ x < 1),(1/2",", "for" ≤ x < 2),(x/4",", "for" 2 ≤ x < 4),(1",", "for" x ≥ 4):}`
What is the probability that a person will have to wait (i) more than 3 minutes, (ii) less than 3 minutes and (iii) between 1 and 3 minutes?
Define dicrete random Variable
Explain the terms probability distribution function
Choose the correct alternative:
If the random variable takes negative values, then the negative values will have
The probability function of a random variable X is given by
p(x) = `{{:(1/4",", "for" x = - 2),(1/4",", "for" x = 0),(1/2",", "for" x = 10),(0",", "elsewhere"):}`
Evaluate the following probabilities
P(0 ≤ X ≤ 10)
Let X be a random variable with a cumulative distribution function.
F(x) = `{{:(0",", "if" x < 0),(x/8",", "if" 0 ≤ x ≤ 1),(1/4 + x/8",", "if" 1 ≤ x ≤ 2),(3/4 + x/12",", "if" 2 ≤ x < 3),(1",", "for" 3 ≤ x):}`
Compute: (i) P(1 ≤ X ≤ 2) and (ii) P(X = 3)