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A random variable ‘X’ is uniformly distributed in the interval [-2, 3] . Another random variable Y is related to random variable X as Y =2X+3. The value of variance of Y is
- a)5.21
- b)6.33
- c)8.33
- d)10.51
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A random variable ‘X’ is uniformly distributed in the interval [-2, 3...
Approach to solution:
Given information:
- Random variable X is uniformly distributed in the interval [-2, 3]
- Random variable Y is related to X as Y = 2X + 3
Finding the mean and variance of Y:
1. The mean of Y can be calculated as E[Y] = E[2X + 3] = 2E[X] + 3
2. Since X is uniformly distributed in the interval [-2, 3], the mean of X is (3 - 2) / 2 = 0.5
3. Therefore, E[Y] = 2(0.5) + 3 = 4
4. To find the variance of Y, we use Var[Y] = Var[2X + 3] = 4Var[X]
5. The variance of X in a uniform distribution is calculated as Var[X] = (b - a)^2 / 12, where a = -2 and b = 3
6. Var[X] = (3 - (-2))^2 / 12 = 25 / 12
7. Therefore, Var[Y] = 4 * (25 / 12) = 100 / 12 = 8.33
Conclusion:
The variance of random variable Y, when Y = 2X + 3 and X is uniformly distributed in the interval [-2, 3], is 8.33. Hence, the correct answer is option 'C'.
Given information:
- Random variable X is uniformly distributed in the interval [-2, 3]
- Random variable Y is related to X as Y = 2X + 3
Finding the mean and variance of Y:
1. The mean of Y can be calculated as E[Y] = E[2X + 3] = 2E[X] + 3
2. Since X is uniformly distributed in the interval [-2, 3], the mean of X is (3 - 2) / 2 = 0.5
3. Therefore, E[Y] = 2(0.5) + 3 = 4
4. To find the variance of Y, we use Var[Y] = Var[2X + 3] = 4Var[X]
5. The variance of X in a uniform distribution is calculated as Var[X] = (b - a)^2 / 12, where a = -2 and b = 3
6. Var[X] = (3 - (-2))^2 / 12 = 25 / 12
7. Therefore, Var[Y] = 4 * (25 / 12) = 100 / 12 = 8.33
Conclusion:
The variance of random variable Y, when Y = 2X + 3 and X is uniformly distributed in the interval [-2, 3], is 8.33. Hence, the correct answer is option 'C'.
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Community Answer
A random variable ‘X’ is uniformly distributed in the interval [-2, 3...
Given that random variable is uniformly distributed in the interval[-2, 3] .
PDF of X is as shown below,
Given, Y=2X+3
Var (Y)= Var (2X)+Var(3)
Var (Y) =22 Var (X)+0
Var (Y) = 4Var (X)
Var (Y) =4*25/12=8.33
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A random variable ‘X’ is uniformly distributed in the interval [-2, 3] . Another random variable Y is related to random variable X as Y =2X+3. The value of variance of Y isa)5.21b)6.33c)8.33d)10.51Correct answer is option 'C'. Can you explain this answer?
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