Advertisements
Advertisements
प्रश्न
Distinguish between discrete and continuous random variables.
Advertisements
उत्तर
| Points of Difference | Discrete Variable | Continuous Variable | |
| 1. | Meaning | A variable which can take only certain specific values. | A variable which can take any value within a given range or limit. |
| 2. | Nature of Values | Its values increase in jumps or steps (whole numbers). | Its values increase continuously, not in jumps or steps. |
| 3. | Example | Number of students in a class – 30, 35, 40, 45, 50. | Height, weight, or age – e.g., 50.5 kg, 42.8 kg, 18.6 years. |
| 4. | Probability Distributions | Binomial, Poisson, and hypergeometric distributions belong to this category. | Normal, Student’s t, and Chi-square distributions belong to this category. |
APPEARS IN
संबंधित प्रश्न
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
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):}`
Is the distribution function continuous? If so, give its probability density function?
Define dicrete random Variable
Explain the distribution function of a random variable
Choose the correct alternative:
A variable that can assume any possible value between two points is called
Choose the correct alternative:
A formula or equation used to represent the probability distribution of a continuous random variable is called
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)
The p.d.f. of X is defined as
f(x) = `{{:("k"",", "for" 0 < x ≤ 4),(0",", "otherwise"):}`
Find the value of k and also find P(2 ≤ X ≤ 4)
The probability density function of a continuous random variable X is
f(x) = `{{:(a + bx^2",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
where a and b are some constants. Find Var(X)
