Advertisements
Advertisements
प्रश्न
The following table is describing about the probability mass function of the random variable X
| x | 3 | 4 | 5 |
| P(x) | 0.2 | 0.3 | 0.5 |
Find the standard deviation of x.
Advertisements
उत्तर
Let x be the random variable taking the values 3, 4, 5
E(x) = Σpixi
= (0.1 × 3) + (0.1 × 4) + (0.2 × 5)
= 0.3 + 0.4 + 1.0
E(x) = 1.7
E(x2) = Σpixi2
= (0.1 × 32) + (0.1 × 42) + (0.2 × 52)
= (0.1 × 9) + (0.1 × 16) + (0.2 × 25)
E(x2) = 7.5
Var(x) = E(x2) – (E(x)]2
= 7.5 – (1.7)2
= 7.5 – 2.89
Var(x) = 4.61
Standard deviation (S.D) = `sqrt("var"(x))`
= `sqrt(4.61)`
σ = 2.15
APPEARS IN
संबंधित प्रश्न
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(2(x - 1), 1 < x ≤ 2),(0, "otherwise"):}`
Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X
A lottery with 600 tickets gives one prize of ₹ 200, four prizes of ₹ 100, and six prizes of ₹ 50. If the ticket costs is ₹ 2, find the expected winning amount of a ticket
Choose the correct alternative:
Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins ₹ 36, otherwise he loses ₹ k2, where k is the face that comes up k = {1, 2, 3, 4, 5}. The expected amount to win at this game in ₹ is
Find the expected value for the random variable of an unbiased die
In a business venture a man can make a profit of ₹ 2,000 with a probability of 0.4 or have a loss of ₹ 1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?
The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f.
f(x) = `{{:(1/30 "e"^(- x/30)",", "for" x > 0),(0",", "for" x ≤ 0):}`
Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point
Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5?
Choose the correct alternative:
A discrete probability distribution may be represented by
The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function
f(x) = `{{:(2"e"^(-2x)",", x > 0),(0",", "otherwise"):}`
Find the expected life of this piece of equipment
