Practice Math Statistics Problems and Master the Concepts

The random variables X and Y have joint density function
f(x,y)=12xy(1-x) 0<x<1,0<y<1
and equal to 0 otherwise.
Find Var(X).

chanyingsauu7 2021-11-07

Let X be a normal random variable with mean 12 and variance 4. Find the value of c such that P[X>c]=.10.

York 2021-11-07

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 $P [X + Y \leq 1]$

verskalksv 2021-11-06

If X is a normal random variable with parameters
$μ = 10$
and
$σ^{2} = 36$
, compute P[X>5]

Emeli Hagan 2021-11-06

Which of the following applies to the Significance Test for the Proportion's underlying assumptions?
1) Data is Categorical.
2) Data is from a convenience sample.
3) $n p_{0}$ and $(1 - p_{0})$ are both greater than 15
4) Data is Quantitative
5) Data is from a Normal Distribution
6) Data is from a random sample
7) $\hat{n p}$ and $n (1 - \hat{p})$ are both greater than 15

EunoR 2021-11-06

Let $X_{1} \dots ., X_{n} and Y_{1}, \dots, Y_{m}$ be two sets of random variables. Let $a_{i}, b_{j}$ be arbitrary constant.
Show that
$C o v (\sum_{i = 1}^{n} a_{i} X_{i}, \sum_{j = 1}^{m} b_{j} Y_{j}) = \sum_{i = 1}^{n} \sum_{j = 1}^{m} a_{i} b_{j} C o v (X_{i}, Y_{j})$

alesterp 2021-11-06

Using the Standard Normal Table from the online lectures this week, what is the area under the standard normal curve:
a) To the left of a z-score of 1.25
b) To the right of a z-score of 1.25
c) Between the z-scores -0.25 and 0.55

Ramsey 2021-11-05

Determine whether the statement is true or false. If it is false, rewrite it as a true statement: "when each data class has the same frequency, the distribution is symmetric."

sibuzwaW 2021-11-05

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 $P [min (X, Y) \geq 2]$

Brennan Flores 2021-11-04

Compute the distribution of X+Y in the following cases:
X and Y are independent normal random variables with respective parameters $(μ_{1}, σ_{1}^{2}) and (μ_{2}, σ_{2}^{2})$ .

Trent Carpenter 2021-11-03

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 conditional density of X
Find the conditional density of Y

Dolly Robinson 2021-11-03

For continuous random variables X and Y with joint probability density function
$f (x, y) = {\begin{cases} x e^{- (x + x y)} & x > 0 a n d y > 0 \\ 0 & o t h e r w i s e \end{cases}$
Find P(X>1 and Y>1).

sanuluy 2021-11-01

Assume that X and Y are jointly continuous random variables with joint probability density function given by
$f (x, y) = b e g \in {c a s e s} \frac{1}{36} (3 x - x y + 4 y) if 0 < x < 2 and 1 < y < 3 ∖ 0 o t h r e w i s e e n d {c a s e s}$
Find the marginal density functions for X and Y .

Suman Cole 2021-11-01

Two random variables X and Y with joint density function given by:
$f (x, y) = {\begin{cases} \frac{1}{3} (2 x + 4 y) & 0 \leq x, \leq 1 \\ 0 & e l s e w h e r e \end{cases}$
Find the marginal density of X.

generals336 2021-10-28

Suppose that the random variables X and Y have joint p.d.f.
$f (x, y) = {\begin{cases} k x (x - y), 0 < x < 2, - x < y < x \\ 0, e l s e w h e r e \end{cases}$
Find the marginal p.d.f. of the two random variables.

banganX 2021-10-28

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

nitraiddQ 2021-10-28

Random variable X and Y have the joint PDF
$f_{X Y} (x, y) = {\begin{cases} c, x \geq 0, y \geq 0, (x^{2} + y) \leq 1, \\ 0, o t h e r w i s e \end{cases}$
Find the marginal PDF $f_{Y} (y)$ .

Chesley 2021-10-27

At a research facility that designs rocket engines, researchers know that some engines fail to ignite as a result of fuel system error. From a random sample of 40 engines of one design, 14 failed to ignite as a result of fuel system error. From a random sample of 30 engines of a second design, 9 failed to ignite as a result of fuel system error. The researchers want to estimate the difference in the proportion of engine failures for the two designs. Which of the following is the most appropriate method to create the estimate?
A one-sample z-interval for a sample proportion A
A one-sample z-interval for a population proportion B
A two-sample z-interval for a population proportion C
A two-sample z-interval for a difference in sample proportions D
A two-sample z-interval for a difference in population proportions

bobbie71G 2021-10-27

True or False? A Kruskal-Wallis test is used to compare a continuous outcome in more than two independent samples.

CMIIh 2021-10-27

Trucks are used in many configurations. Three common configurations are tractors with 1, 2, and 3 trailers. Accident statistics for these configurations in 2002 are listed below.
Fatal U.S. Truck Accidents in 2002 by Configuration
$\begin{array}{cc} Truck Configuration & Number of Registered Vehicles & Number of Accidents \\ Tractor, 1 trailer & 150, 000 & 2, 889 \\ Tractor, 2 trailers & 5, 100 & 154 \\ Tractor, 3 trailers & 200 & 1 \end{array}$
Assume these statistics represent simple random samples for each configuration. Which of the following would be the most, appropriate test to use to determine whether the populations for each configuration have the same rate of fatal accidents?
A) One-sample proportion z-test.
B) Two-sample proportion z-test
C) Chi-square test for independence
D) Chi-square goodness-of-fit test
E) Chi-square test for homogeneity of proportions

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