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प्रश्न
Distinguish between discrete and continuous random variables.
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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. |
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संबंधित प्रश्न
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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 following probability function.
P(X = x) = `{{:("k"x, x = 2"," 4"," 6),("k"(x - 2), x = 8),(0, "otherwise"):}`
where k is a constant. Show that k = `1/18`
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| Value of X = x |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
Evaluate p(x < 6), p(x ≥ 6) and p(0 < x < 5)
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.
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?
Explain the terms probability density function
What are the properties of discrete random variable
Choose the correct alternative:
A variable that can assume any possible value between two points is called
Choose the correct alternative:
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