Recent questions in Random variables

College StatisticsOpen question

Eisregiony1 2022-08-18

A population of values has a normal distribution with $\mu =67.9$ and $\sigma =44.8$ . You intend to draw a random sample of size n=17.

Find the probability that a single randomly selected value is greater than 94

Find the probability that a single randomly selected value is greater than 94

College StatisticsOpen question

Nashorn0o 2022-08-18

Find the following probabilities for a standard normal random variable z : P(-1 <= z<= 1)

College StatisticsOpen question

Cecilia Tapia 2022-08-18

Find the following probabilities for a standard normal random variable z : P(z> 1)

College StatisticsOpen question

nascarchic839e9 2022-08-17

A population is normally distributed with $\mu =100$ and $\sigma =25$ .

Find the probability that a value randomly selected from this population will have a value greater than 135.

Find the probability that a value randomly selected from this population will have a value greater than 135.

College StatisticsOpen question

Erin Larsen 2022-08-17

Let X and Y be continuous random variables with joint density function

$f(x,y)=\{\begin{array}{ll}\frac{x}{5}+cy& 0<x<1,1<y<5\\ 0& otherwise\end{array}$

where c is a constant. Are X and Y independent?

College StatisticsOpen question

autumnunfound91 2022-08-17

The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter $\lambda =1$ .

What is the conditional probability that a repair takes at least 3 hours, given that its duration exceeds 2 hours?

What is the conditional probability that a repair takes at least 3 hours, given that its duration exceeds 2 hours?

College StatisticsAnswered question

Capriconian321 2022-08-08

A random variable follow a normal distribution with mean 12 and variance 2.5. Find upper quartile

College StatisticsAnswered question

Pooja Singh2022-08-05

Suppose the cumulative distribution of random variable X is F(x) 0 x< 0 0.2 x 0 <= x < 5 1 5 <=x Determine the following: (a) P (X < 2.8) (b) P (X > 1.5) (c) P (X < -2) (d) P (X > 6)

College StatisticsAnswered question

Markus Petty 2022-07-20

Suppose ${X}_{1},\dots ,{X}_{m}$ and ${Y}_{1},\dots ,{Y}_{n}$ are random variables with the property that $Cov({X}_{i},{Y}_{j})<\mathrm{\infty}$ for all i and j. Show that, for any constants ${a}_{1},\dots ,{a}_{m}$ and ${b}_{1},\dots ,{b}_{n}$,

$Cov(\sum _{i=1}^{m}{a}_{i}{X}_{i},\sum _{j=1}^{n}{b}_{j}{Y}_{j})=\sum _{i=1}^{m}\sum _{j=1}^{n}{a}_{i}{b}_{j}Cov({X}_{i},{Y}_{j})$

$Cov(\sum _{i=1}^{m}{a}_{i}{X}_{i},\sum _{j=1}^{n}{b}_{j}{Y}_{j})=\sum _{i=1}^{m}\sum _{j=1}^{n}{a}_{i}{b}_{j}Cov({X}_{i},{Y}_{j})$

College StatisticsAnswered question

jayeshmahadik6879 2022-07-19

when normal distribution curve is more flatter in the case on

College StatisticsAnswered question

Tamia Edwards2022-07-07

The GPA of Students at the University has a normal distributed with a mean of 3.62 and a variance of 6.25.

a. Calculate the probability that for a randomly select student, the GPA will be more than 3.99.

College StatisticsAnswered question

Shreya Khamrai2022-07-03

What is the probability that there will be strictly more heads than tails out of 10 flips

of a fair coin? Out of 20 flips?

College StatisticsOpen question

Aamyia Bullock2022-06-29

A restaurant offers a $12 dinner special that has

4

choices for an appetizer,

11

choices for an entrée, and

3

choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert?

College StatisticsAnswered question

Eslam Tail2022-06-16

Toss 3 coin and 2 die find the probability of appearing 3 heads and sum of a dot = 12

College StatisticsAnswered question

Harrison Kikuyu2022-05-08

Jane chooses a number X at random from the set of numbers

{1, 2, 3, 4}, so that

P(X = k) =

1

4

for k = 1, 2, 3, 4.

She then chooses a number Y at random from the subset of

numbers {X, ...,

4

}; for example, if

X = 3, then Y is chosen at

random from {

3,

4}

.

(i) Find the joint probability distribution of X and Y and display

it in the form of a two-way table.

[5 marks]

(ii) Find the marginal probability distribution of Y , and hence

find E(Y ) and V ar(Y ).

[4 marks]

(iii) Show that Cov(X, Y ) = 5/8.

[4 marks]

(iv) Find the probability distribution of U = X + Y . [7

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.