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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
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.
Distinguish between discrete and continuous random variables.
Explain the terms probability distribution function
Choose the correct alternative:
If c is a constant, then E(c) is
Choose the correct alternative:
A variable which can assume finite or countably infinite number of values is known as
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)
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)
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):}`
Is X a discrete random variable? Justify your answer
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)
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)
