# random

1. ### Expectation of random variable

Hi, How to prove that $E[X]=\displaystyle\int_0^{\infty}P(X>t)dt$ Answer: $But E[x]=\displaystyle\int_0^\infty xf(x)dx$ How to proceed further? How to arrive at L.H.S.?
2. ### Probability density function of sum 3 dependent random variables?

Suppose we have s = x+y+z and x,y and z are dependent random variables. Can I use this approach to find probability density function of S? first find CDF of S: $F_{S}(s)=P(S<=s)=\int_{-\infty}^{+\infty}dx \int_{-\infty}^{s-x}dy \int_{-\infty}^{s-x-y}f_{X,Y,Z}(x,y,z)dz$ and then differentiate it...
3. ### Mixed random variables with conditional probability constraints

Can someone please look at this problem statement in the attached photo and then explain the approach to solve such a problem my main problem with this question is I don't know to to find the probability when given multiple random variables also how do you take into account the conditionality...
4. ### Random sample Poisson distribution

Hello, I was hoping someone could help explain how to do this problem. I am pretty stuck. Thanks! X1....X50 is a random sample with Poisson distribution with lamba = 5. What is P(4.5 <= Xbar <= 5.3)?
5. ### Function of uniform random variable.

Hello this is the problem I'm working on. a voltage X is uniformly distributed in the set {-3,-2,-1,0,1,2,3,4} A. Find the pdf and CDF of the random variable X. for this question I found the pdf as [[pdf=1/7 for -3<=X<=4 and 0 else]] also I found the CDF as [[ CDF= (X+3)/7 for...
6. ### Random Samples with normal distribution given mean and variance

Hello! So I know this problem should be super easy but for some reason I can't figure out how to do it. Any formulas/direction/etc is appreciated Suppose X1.....Xn are random samples from normal distribution with mean u and variance r2 When n=10, calculate P(x bar is within u plus or minus...
7. ### Joint Distribution of iid Random Variables

Hi, Let X,Y,Z be independent, identically distributed random variables,each with density$f(x)=6x^5$ for $0 \leq x\leq 1$ and 0 elsewhere.I want to find the distribution and density functions of the maximum of X,Y and Z. Answer:-I know by integrating density function, distribution function can...
8. ### Finding the covariance of two random variables X and Y

I understand all the steps but i don't know where the marginal density function for g(x) and h(y) (highlighted in yellow) came from. Can someone explain?
9. ### Matching moments of distributions of a random variable x and a transformation x1=x^2

My statistics have become a bit rusty. I am puzzled with a problem. Let assume that x is a random variable and can either x ~ Normal(0,1) or x ~ Uniform(a,b) From Normal : E(x) = 0, V(x) = 1 From Uniform : E(x) = 1 / (a+b), V(x) = 12 / ( (b-a)^(2) ) If we want to match the mean and the...
10. ### Show that a random process is WSS

Can anyone explain the last step in the solution, the delta function. I know this should be super obvious but i just cant figure it out right now... Im thinking you need to integrate and the sines are zero...
11. ### Proving the random walk??

Usually when one monitories a stock market, one wishes to find a trend in order to be able to predict the price and make some money in the process. My problem is the opposite. I have pattern that resembles a random walk, it is a set of values (40-50 values) measured at different time points...
12. ### Finding the distribution of the random variable from function?

Hi, Can anyone please find the CDF and PDF of the random variables from the following functions in any way?
13. ### Distribution function of random variable

Hi! I would really like to get some help with the following problem: "A man lives by a bus stop from which he takes a bus to his job. The journey takes 20 minutes and the buses comes with a 10 minute interval. One certain morning he plans to be at work at 8:30 and not later. He needs 20 minutes...
14. ### Normalization of Two Mean Random Variables

Hello, I am dealing with the following question: My question is, once we Find X_1 - X_2 do I treat their normal distribution as, say X_3 and do the usual standardization procedure? I have attached my attempt at the problem, could someone please verify if I'm on the right track. Thank you...
15. ### pdf for continuous random variable

Hello again everyone, I'm having some trouble understanding an example for a probability density function of a cont. RV. The part I'm not getting is the integrals. I need an elaboration on what is going on with the calculations so I can see what is happening. I assume that it has something to...
16. ### Random Sampling Questions

Hello, I have tried the above question, but my answers do not seem correct. My probabilities are all 0 or 1. If anyone could provide some guidance, I would really appreciate it! PDF: Thank you.
17. ### Binomial Random Variable Probabilities

The problems states X is a binomial random variable, n=25 and p=0.8. Asks for the standard deviation of X. Any clue how this would be solved?
18. ### Find the distribution of the random variable

Find the distribution of the random variable $Y=\sum _{j=0}^{d\:}\:X^2_j$ if $X^2_1,\:X^2_2,\:.....,\:X^2_d$ are all independent and distributed with a chi-squared distribution with $v=1$ degree of freedom, Say, $X^2_j\:$~$\:X^2_1,\:j=1,.....,d$ How do I solve this question ?
19. ### Find the density of the random variable Y=X^2

Find the density of the random variable Y=X^2, if the random variable X follows a standard normal distribution. I think I should use mgf to solve it is that right ? what should I do to start ?
20. ### Normal Random Variable

Hello, I'm not sure what N(0,4) means and how to deal with the absolute value of X. We haven't learned this in detail yet, and I'm just wondering how to solve such problem. Thank you.