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Results tagged with self-study
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user 72126
A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.
0
votes
0
answers
71
views
iid random variables [duplicate]
Let X,Y,Z be independent, identically distributed random variables,each with density $f(x)=6x^5$ for $0\leq x\leq1$ and 0 elsewhere.I want to find the distribution and density functions of the maximum …
- 1,226
3
votes
1
answer
96
views
Probability theory
Suppose that $A$ and $B$ are independent of each other, equally likely to be any of the $2^n$ subsets of $\{1, \ldots , n \}$,I want to find
a) $P(A\subset B)$.
b) $P(A \cap B) = \varnothing$.
Answ …
- 1,226
2
votes
1
answer
157
views
Conditional probability questions
Three dice are rolled. If no two show the same face, what is the probability that one is an ace?
Given that a throw with ten dice produced at least one ace, what is the probability p of two or more a …
- 1,226
2
votes
0
answers
167
views
Exponential distribution question
Let X and Y be independent exponential random variables with respective rate $\lambda$ and $\mu$ let c be a positive constant.
I want to find out a) $E[min(X,Y)|X>c]$
b)$E[min(X,Y)|X>Y+c]$ by a dire …
- 1,226
2
votes
0
answers
54
views
Trials,outcomes and their expectation
Consider a sequence of independent trials, each of which is equally likely to result in
any of the outcomes 0, 1, . . . ,m. Say that a round begins with the first trial, and that
a new round begins ea …
- 1,226
-1
votes
1
answer
35
views
Patient, Doctor and flu vaccination [closed]
The Department of Health encourages young children to have a flu vaccination each year. The vaccination reduces the likelihood of getting a flu from 40% to 10%. If 45% of the young children visiting t …
- 1,226
0
votes
0
answers
309
views
Realisation of at least one event among N events
Two dice are thrown r times. I want to find the probability $p_r$ that each of the six combinations (1,1),...,(6,6)appears at least once.
My Answer:-$p_r=6*(1-(\frac{35}{36})^r)-15*(1-(\frac{34}{36}) …
- 1,226
7
votes
3
answers
2k
views
Poisson random variable self-study question
You are invited to a party. Suppose the times at which invitees arrives are independent uniform(0,1) random variables. Suppose that aside from yourself the number of other people who are invited is a …
- 1,226
3
votes
1
answer
687
views
Expectation and variance of Uniform Distribution
If X is uniformly distributed over (0,1),I want to calculate $E[X^2],E[X^n]$ and $Var[X^n]$
Answer:I tried to get 2nd derivative of mgf $\frac{e^{tb}-e^{ta}}{t(b-a)}$ to compute $E[X^2]$.
I tried t …
- 1,226
0
votes
1
answer
2k
views
Random walk based on coin toss [closed]
You are in an open field with two coins and you alternate flipping the coins and taking steps by the following rules:
If both coins are heads, then you take one step north.
If both coins are tails, …
- 1,226
1
vote
Accepted
Random walk based on coin toss
The answer provided on the other math website is as follows.
There are four outcomes of the tossings of the two fair coins, namely, $HH,HT, TH,TT$.
As there are 20 steps, the total numbers of outcom …
- 1,226
1
vote
1
answer
217
views
Probability and Counting
Suppose You are ordering two pizzas.A pizza can be small,medium,large or extra large,with any combination of 8 possible toppings( getting no toppings is allowed, as is getting all 8) How many possibil …
- 1,226
1
vote
1
answer
81
views
Moment of Z (about 0) in Arcsine distribution
Moments of Z (about 0) are
$E(Z^n)=\int\limits_0^{\pi/2}\frac{2}{\pi}sin^{2n}\theta d\theta=\prod\limits_{j=0}^{n-1}\frac{2j+1}{2j+2}$
Would any stats expert explain me how the R.H.S is arrived at?
- 1,226
1
vote
1
answer
231
views
Expected Number of steps
At each stage a person either moves one step to the right with probability 0.6 or one step to the left with probability 0.4.Assuming the direction of each step is independent
I want to find the expec …
- 1,226
1
vote
1
answer
135
views
Multinomial Probability Question
A lift starts with 5 passengers and stops at 8 floors. Find the probability that no two or more passengers leave at the same floor. Assume that all arrangements of discharging passengers have the same …
- 1,226