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What are the properties of discrete random variable - Business Mathematics and Statistics

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प्रश्न

What are the properties of discrete random variable

बेरीज
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उत्तर

The probability mass function p(x) must satisfy the following conditions

(i) p(xi) ≥ 0 ∀ i

(ii) `sum_("i" = 1)^oo "p"(x_"i")` = 1

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Random Variable
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Random Variable and Mathematical expectation - Exercise 6.1 [पृष्ठ १३३]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
पाठ 6 Random Variable and Mathematical expectation
Exercise 6.1 | Q 19. (i) | पृष्ठ १३३

संबंधित प्रश्‍न

Two balls are chosen randomly from an urn containing 6 red and 8 black balls. Suppose that we win ₹ 15 for each red ball selected and we lose ₹ 10 for each black ball selected. X denotes the winning amount, then find the values of X and number of points in its inverse images


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 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 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.


Explain what are the types of random variable?


Describe what is meant by a random variable


Explain the terms probability density function


What are the properties of continuous random variable?


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):}`
Is X a discrete random variable? Justify your answer


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