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प्रश्न
Explain what are the types of random variable?
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उत्तर
Random variables are classified into two types namely discrete and continuous random variables these are important for practical applications in the field of Mathematics and Statistics.
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संबंधित प्रश्न
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`
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.
Define random variable
Explain the terms probability Mass function
What are the properties of continuous random variable?
Choose the correct alternative:
If c is a constant in a continuous probability distribution, then p(x = c) is always equal to
Choose the correct alternative:
The probability density function p(x) cannot exceed
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(X ≤ 0)
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)
Consider a random variable X with p.d.f.
f(x) = `{(3x^2",", "if" 0 < x < 1),(0",", "otherwise"):}`
Find E(X) and V(3X – 2)
