Random Variable Problems & Solutions

Consider two continuous random variables X and Y with joint density function
$f (x, y) = {\begin{cases} x + y o \leq x \leq 1, 0 \leq y \leq 1 \\ 0 o t h e r w i s e \end{cases}$
$P (X > 0.8, Y > 0.8)$ is?

Albarellak 2021-06-03

Compute the distribution of $X + Y$ in the following cases:
X and Y are independent Poisson random variables with means respective $λ_{1} a n d λ_{2}$ .

Wierzycaz 2021-06-02

Suppose that X and Y are continuous random variables with joint pdf $f (x, y) = e^{- (x + y)} 0$ and zero otherwise.
Find $P (X > Y)$

banganX 2021-06-02

The joint density of the random variables X and Y is given by
$f (x, y) = {\begin{cases} 8 x y & 0 \leq x \leq 1, 0 \leq y \leq x \\ 0 & o t h e r w i s e \end{cases}$
Find the marginal density of X

Rivka Thorpe 2021-06-01

The continuous random variables X and Y are statistically independent and have marginal density functions $f_{X} (x) = 2 x, 0 \leq x \leq 1, f_{Y} (y) = \frac{1}{y^{2}}, y \geq 1$ .
Calculate the probability $P (X \leq 0.5, Y \leq 2) =$ ?

Khadija Wells 2021-06-01

How many different 10 letter words (real or imaginary) can be formed from the following letters
H,T,G,B,X,X,T,L,N,J

opatovaL 2021-06-01

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: $X + Y$

babeeb0oL 2021-05-31

Suppose that the random variables X and Y have joint p.d.f.
$(f (x, y) = {\begin{cases} k x (x - y) \\ 0 \end{cases}$ Find the marginal p.d.f. of the two random variables.

Brennan Flores 2021-05-31

For continuous random variables X and Y with joint probability density function
$f (x, y) = {\begin{cases} x e^{- (x + x y)} & x > 0 a n d y > 0 \\ 0 & o t h e r w i s e \end{cases}$
Are X and Y independent? Explain.

nitraiddQ 2021-05-30

Gender and housing Using data from the 2000 census, a random sample of 348 U.S. residents aged 18 and older was selected. The two-way table summarizes the relationship between gender and housing status for these residents. $\begin{array}{lr} Gender \\ Housingstatus Housing status & \begin{array}{cccc} Male & Female & Total \\ Own & 132 & 122 & 254 \\ Rent & 50 & 44 & 94 \\ Total & 182 & 166 & 348 \end{array} \end{array}$ State the hypotheses for a test of the relationship between gender and housing status for U.S. residents.

OlmekinjP 2021-05-30

Random variables X and Y have joint PDF
$f_{X, Y} (x, y) = {\begin{cases} 12 e^{- (3 x + 4 y)}, x \geq 0, y \geq 0 \\ 0, o t h e r w i s e \end{cases}$
Find $P [m a x (X, Y) \leq 0.5]$

avissidep 2021-05-28

Random variables X and Y have joint PDF
$f_{X, Y} (x, y) = {\begin{cases} 12 e^{- (3 x + 4 y)}, x \geq 0, y \geq 0 \\ 0, o t h e r w i s e \end{cases}$
Find $P [X + Y \leq 1]$

Wierzycaz 2021-05-28

If X and Y have the same independent distributions with mean $μ$ and variance $σ^{2}$ , find $E [(X - Y)^{2}]$

chillywilly12a 2021-05-28

Random variables X and Y have joint PDF
$f_{X, Y} (x, y) = {\begin{cases} 12 e^{- (3 x + 4 y)}, x \geq 0, y \geq 0 \\ 0, o t h e r w i s e \end{cases}$
Find $P [m i n (X, Y) \geq 2]$

foass77W 2021-05-27

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 0.5Y

a2linetagadaW 2021-05-26

Random variables $X_{1}, X_{2}, . . ., X_{n}$ are independent and identically distributed. 0 is a parameter of their distribution.
If $X_{1}, X_{2}, . . ., X_{n}$ are Normally distributed with unknown mean 0 and standard deviation 1, then $\overset{―}{X} \sim N (\frac{0, 1}{n})$ . Use this result to obtain a pivotal function of X and 0.

Kyran Hudson 2021-05-25

The area enclosed by the x and y axes has a uniform distribution of the random variables X and Y, and the curve $y = 1 - x^{2}$ .
Compute E. (XY)

opatovaL 2021-05-23

Random variables $X_{1}, X_{2}, . . ., X_{n}$ are independent and identically distributed. 0 is a parameter of their distribution.
If $q (X, 0) \sim N (0, 1)$ is a pivotal function for 0, explain how you would use this result to obtain a symmetrical 95% confidence interval for 0.

nagasenaz 2021-05-23

Suppose that X and Y are continuous random variables with joint pdf $f (x, y) = e^{- (x + y)} 0$ and zero otherwise.
Find $P (X > 3)$

Bevan Mcdonald 2021-05-23

Compute the distribution of X+Y in the following cases:
X and Y are independent binomial random variables with parameters (n,p) and (m,p).

When you have an equation that deals with random variables, always start with an explanation related to some random variable examples. It is what the majority of skilled engineers do because it is the only way how one can avoid mistakes when working with statistical data. Even though this part of statistics and probability may seem overly complex, approach every random variable equation through the lens of probability as you seek answers to your questions. Compare provided solutions, see similarities, and you will achieve the most efficient solutions.

Explore Random Variables: Examples & Equations