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प्रश्न
Distinguish between discrete and continuous random variables.
उत्तर
| Discrete Variable | Continuous Variable |
| 1. A variable which can take only certain values. | 1. A variable which can take any value in a particular limit. |
| 2. The value of the variables can increase incomplete numbers. | 2. Its value increases infractions but not in jumps. |
| 3. Example: Number of students who opt for commerce in class 11, say 30, 35, 40, 45, and 50. | 3. Example: Height, Weight and age of family members: 50.5 kg, 30 kg, 42.8 kg and 18.6 kg. |
| 4. Binomial, Poisson, Hypergeometric probability distributions come under this category. | 4. Normal, student’s t and chi-square distribution come under this category. |
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संबंधित प्रश्न
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.
Two coins are tossed simultaneously. Getting a head is termed a success. Find the probability distribution of the number of successes
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 |
Find k
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 |
Evaluate p(x < 6), p(x ≥ 6) and p(0 < x < 5)
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?
Explain what are the types of random variable?
Explain the terms probability density function
Explain the terms probability distribution function
What are the properties of discrete random variable
