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
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.
The length of time (in minutes) that a certain person speaks on the telephone is found to be random phenomenon, with a probability function specified by the probability density function f(x) as
f(x) = `{{:("Ae"^((-x)/5)",", "for" x ≥ 0),(0",", "otherwise"):}`
What is the probability that the number of minutes that person will talk over the phone is (i) more than 10 minutes, (ii) less than 5 minutes and (iii) between 5 and 10 minutes
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
What are the properties of continuous random variable?
Choose the correct alternative:
A formula or equation used to represent the probability distribution of a continuous random variable is called
Choose the correct alternative:
If we have f(x) = 2x, 0 ≤ x ≤ 1, then f(x) is a
Choose the correct alternative:
A set of numerical values assigned to a sample space is called
Choose the correct alternative:
The probability density function p(x) cannot exceed
