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Standard deviation of a random variable between (0,1]

score 76 · Answer 1 · 2026-03-26 19:25:21

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Standard deviation of a random variable between (0,1]

Published on 26 Mar 2026 - 19:25

score 26 · Answer 2 · 2026-03-30 00:53:08

26

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Show $\mathrm{Var} \big( c_1 X + c_2 Y + c_3 XY + c_4 X^2 + c_5 Y^2 \big) > 0$ for any not all zero $c_i$ where $(X, Y) \sim Normal$

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score 110 · Answer 3 · 2018-09-30 13:53:27

110

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score 22 · Answer 6 · 2018-09-30 21:10:30

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score 34 · Answer 9 · 2018-10-01 20:58:44

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score 191 · Answer 10 · 2026-02-23 04:51:51

191

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score 26 · Answer 11 · 2018-10-02 04:06:21

26

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$Var(a_1X^2 + a_2X) > 0$ whenever $(a_1 , a_2) \neq 0$ where $X \sim N(\mu, \sigma^2)$

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score 49 · Answer 12 · 2026-03-25 14:25:52

49

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score 42 · Answer 13 · 2018-10-02 13:40:18

42

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Real-Life Probability Question

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score 34 · Answer 15 · 2018-10-03 09:18:37

34

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List Question

Standard deviation of a random variable between (0,1]

Show $\mathrm{Var} \big( c_1 X + c_2 Y + c_3 XY + c_4 X^2 + c_5 Y^2 \big) > 0$ for any not all zero $c_i$ where $(X, Y) \sim Normal$

uniform random numbers and pdf and cdf

Proof of a simple theorem on measurability

How can I find this probability of multiple Random Variables?

Defining a random variable with two given conditions and determining whether it's unique.

Sequence of random variable converges to zero but expectation converges to infinity

On the random variables and conditional probability

How to prove $\sum_{i\geq 1}N_i<\infty$ almost surely? Given $N_i$ are poisson rv with intensity $np_i$ where $\sum_{i\geq 1}p_i=1$

Coupon Collector problem - 2nd moment method

$Var(a_1X^2 + a_2X) > 0$ whenever $(a_1 , a_2) \neq 0$ where $X \sim N(\mu, \sigma^2)$

Expectation of $E(\frac{(X+Y)^4}{X-Y})$ where X,Y are standard normal distributed

whats wrong in this alternate approach to coupon collector problem

Real-Life Probability Question

How can I show that $Y_n(t)$ is iid again?

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