This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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14 views

Question on probability about collectible cards

Suppose there are 20 different types of collectible cards and suppose that each time you buy a card, it is equally likely to be any one of the 20 types. Let X be the number of types of cards you still ...
0
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1answer
12 views

Conditional Probability Distribution

Let x and y denote the values of two consecutive die roles(6 sided). U=min(x,y) V=max(x,y). Determine the conditional probability mass function for U given V=v.
0
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2answers
20 views

$Pr(X<v)$ on a dice roll

If you have a 6-sided dice, what is the probability of getting less that $k$ on it? I am really trying to figure out the $Pr[U=u \cap V=v]$ but I assume that that is equivalent to calculating $Pr[u ...
0
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0answers
8 views

Help with deriving minimum length confidence bounds for a F distribution variance $\sigma^2$ …

Derive minimum length confidence bounds for a F distribution variance $\sigma^2$ and the ratio of two F distribution population variances $\frac{\sigma_1^2}{\sigma_2^2}$. What I got so far is ...
0
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1answer
16 views

Lack of memory property of probability distributions

According to wikipedia lack of memory property applies to geometric and exponential distributions. I was trying to apply it to binomial distribution. Am I modelling my question correctly? So imagine ...
1
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1answer
23 views

Predicting the number of simple circuits in a graph

If I have a directed graph with $n$ vertices, and the mean number of out-edges per vertex is $x$, what is the expected number of simple circuits that will be found in the graph? What happens to the ...
0
votes
2answers
19 views

how to find f(21) of the following probability generating function

I have a pgf that seems to me would take more than 5 minutes to find f(21) of. Does anyone know how to compute f(21) of this pgf within the specified time? ...
2
votes
3answers
418 views

Probability of Parking Spot Being Empty

A parking spot is unoccupied 1/3 of the time... But, you find it empty for nine consecutive days in a row. Find the probability that it will be empty on the tenth day. Read more: ...
0
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0answers
9 views

Is there any general selection criteria for using a probability distribution?

I have learned that Poisson distribution is used often for queues, while exponential are used for the time between events of a queues. I know for small sample sizes to use the student distribution, ...
0
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1answer
11 views

probability of second highest no in a uniform distribution

Suppose $n$ real no are drawn at random from the uniform distribution over the interval $[0,1]$. For $x$ belongs to $[0,1]$, what is the probability that the second highest number drawn is $<= x$? ...
3
votes
2answers
43 views

Transformation on a random variable

Can someone please help me with formatting this question? $Y$ is an exponential random variable with parameter $1$. Let $Z=-Y$, what is the pdf of $Z$? Attempt: $$\Pr(-Y< y)=\Pr(Y>-y) ,$$ ...
0
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1answer
14 views

probability, depedence => uncorrelated?

One quick question. Two random variables are dependent, so it must be uncorrelated? Also for the terminalogy, does the term "uncorrelated" means two random variables have a corvariance factor of 0? ...
0
votes
1answer
20 views

Question of Buffon's Needle

I looked at the gif on wikipedia that explains Buffon's needle, but I have two questions. First, why do you only consider $x$ as the distance from the center of the needle to the closest line, so it ...
1
vote
1answer
14 views

Probability of at least one card matching when flipping through two separate decks.

Two identical decks consist of 6 white cards and 6 black cards each. The top card of each deck is flipped at the same time. If this is done repeatedly, what is the probability that at least one of the ...
1
vote
1answer
19 views

probability, please help on bayes question

I dont need exact answer, I just need help to judge wether my following method is correct or not. Question:A physician has 5 patients. There are treatments A and B. Physician gives treament A to 3 ...
0
votes
1answer
21 views

probability, at least one is not present

you have $5$ red balls, $10$ green balls, and $15$ yellow balls in a balls. You randomly choose $5$ without replacement. What is the probability that at least one of the $3$ colors is not present ...
0
votes
1answer
9 views

Derive the Cramer-Rao lower bound (CRLB) for any unbiased estimator of $\mu^2$.

Let $Y_1, Y_2, . . . , Y_n$be a random sample from a normal distribution with mean μ and variance 1. Derive the Cramer-Rao lower bound (CRLB) for any unbiased estimator of $\mu^2$. Could anyone ...
0
votes
1answer
17 views

Sum of two independent non-identical uniform random variables

Let's say we have two independent random variables, $X$ is uniform on $[0,1/2]$ and $Y$ is uniform on $[1/2,1]$. If we look at the distribution of $X+Y$, is it triangular distribution between ...
0
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0answers
9 views

Questions related to Rao–Blackwell theorem

In this exercise, we illustrate the direct use of the Rao–Blackwell theorem. Let $Y_1, Y_2, . . . , Y_n$ be independent Bernoulli random variables with $p(y_i | p) = py_i (1 − p)1−y_i , y_i = 0, 1.$ ...
0
votes
1answer
19 views

Multiple Random Variables - Who Wins

For $(a)$ I have figured out that I am looking for the value $P(A<B<C)$. I have done this problem with only two turtles, and I have found that the value is the double integral of the two ...
1
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0answers
17 views

find E($\bar{Y^4})$ by using moment generating function for a normal distribution with mean μ and variance 1.

Let $Y_1, Y_2, . . . , Y_n$be a random sample from a normal distribution with mean μ and variance 1. I would like to find E($\bar{Y^4})$ by using moment generating function. The setup I have right ...
1
vote
1answer
19 views

Calculate the Marginal Probability

f($X_1$, $X_2$| $p_1$, $p_2$) = $p_1^{x_1}$(1-$p_1)^{({n_1}-{x_1})}$$p_2^{x_2}$(1-$p_2)^{({n_2}-{x_2})}$ $p_1$~Unif(0,1) independently $p_2$~Unif(0,1) $n_1$=34 $n_2$=56 Calculate the marginal ...
0
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0answers
29 views

Simplification of Double Integral with Independent Parameters

I am trying to find a posterior distribution and the hint is that the double integral in the denominator should simplify because $p1$ and $p2$ are independent. $\displaystyle \int$$\displaystyle ...
0
votes
1answer
15 views

Moment Generating Function of the Chi-Squared Distribution

The questions wants us to show that the MGF for the chi-squared distribution is equal to I know that to show that I need to evaluate this integral. I'm not sure where to begin to evaluate it. ...
1
vote
1answer
40 views

Bounds for being very far from the mean

If I toss $n$ coins each with probability $1/\sqrt{n}$ of getting a head, I would like to know bounds for the probability of getting $n/2$ or more heads. Clearly the mean number of heads is ...
1
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0answers
29 views

A Simple yet interesting “function of a random variable” question

Given continous density functions $f_0,f_1$ on $\mathbb{R}$ and $Y$, a random variable following the density $f_0$, I am able to calculate the density function $h$, of $\ln l(Y)=\ln(f_1/f_0(Y))$ as ...
1
vote
1answer
22 views

PDF of Sum of Two Random Variables [on hold]

$X$ and $Y$ are uniformly distributed on the unit disk. Thus, $f_{X,Y}(x,y) = \begin{cases} \frac{1}{\pi}, & \text{if} ~ x^2+y^2 \leq 1,\\ 0, &\text{otherwise.}\end{cases}$ If $Z=X+Y$, find ...
0
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0answers
23 views

Acceptance Probability [on hold]

10 Students are applying for postdoctoral position. The employer will only choose one candidate. Student Data 1 (PhD) 2 (MSc) 3 (PhD) 4 (BSc) 5 (BSc) 6 (MSc) 7 (MSc) 8 (BSc) ...
1
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0answers
26 views

Need help finding probability distribution [on hold]

In Cairo $30\%$ of residents listen to the local fm radio. $10$ residents are chosen at random: a) state the distribution of the random variable b) find the smallest value of $s$ so that $\Pr(X \ge ...
1
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0answers
12 views

Find critical Value

A Basketball scout randomly selected 144 players and timed how long each player took to perform a certain drill.The times in this sample were distributed with a mean of 8 minutes. The population ...
0
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0answers
23 views

Probability of events [on hold]

1) 5 cards are selected from a 52-card deck for a poker hand. a) How many simple events are in the sample space? b) A royal flush is a hand that contains the A,K,Q,J, and 10, all in the same suit. ...
0
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1answer
18 views

Likelihood of Two Binomial Distributed RV's

We are given that Let X1~Bin(n1 = 34, p1) and X2~Bin(n2 = 56, p2) In general, what is the likelihood, L(p1, p2) = f (X1, X2 | p1, p2) for the data X1 and X2 I believe that I am supposed to use a ...
1
vote
1answer
12 views

application of the sampling distribution of x

the GBAs of all students enrolled at a large university have an approximately normal ditribution with a mean of 3.02 and a standard deviation of 0.29 ..find the probability that the mean GBA of a ...
-4
votes
1answer
49 views

What is the answer [on hold]

Joe is 80 percent sure that his missing key is in one of the two pockets of his hanging jacket, being 40 percent certain it is in the left-hand pocket and 40 percent certain it is in the right hand ...
3
votes
1answer
1k views

Distribution of the sum of the $q$th largest observations to the sum of total for a power-law.

Where $X_{(1)}, X_{(2)}, \ldots,X_{(n)}$ are sorted independents r.v.s, where we index and order in such a way that $X_{(i)} \geq X_{(i-1)}$, $i>1$ where all realizations follow the same Standard ...
1
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0answers
53 views

Probability Theory (Hypergeometric) [on hold]

Suppose that a sample of size $n$ is to be chosen randomly without replacement from a basket containing $N$ balls, of which $m$ are red. Let $X$ be the number of red balls selected. Derive the ...
0
votes
1answer
20 views

Expectation of conditional event for throwing a fair dice

A fair die (with face numbered $1,\ \ldots\ ,6)$ is independently rolled repeatedly. Let $X$ denote the number of rolls till an even number is seen and let $Y$ denote the number of rolls till $3$ is ...
0
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1answer
15 views

permutations and combination

How many different strings of lights can be created by placing 40 coloured lights on a horizontal string if 12 of them are red, 6 are blue, 14 are green and 8 are yellow? Assume that lights of the same ...
0
votes
1answer
11 views

Bridge hand Combination/Permutation

A Bridge hand consists of 13 cards from a deck of 52 cards. In how many ways can a (bridge) hand consisting of 5 spades(♠), 4 hearts(♥), 4 diamonds(♦) and 0 clubs(♣) be selected?
2
votes
3answers
52 views

What does “twice as likely” mean?

Once in a while I hear people say something like X is twice as likely as Y. What they usually mean is: $$p(X) = 2 \cdot p(Y)$$ and - in the context they refer to - they usually have $p(Y) < ...
0
votes
2answers
30 views

Pobability four letter problem [on hold]

Four different letters $a,b,c,d$ are written and put in the four different envelopes $A,B,C,D$. Find the probability distribution for number of letters put in correct envelopes.
0
votes
1answer
28 views

Urn with $n$ balls, one special

An urn contains n balls, one of which is special. If k of these balls are withdrawn one at a time, with each selection being equally likely to be any of the balls that remain at the time, what is the ...
0
votes
0answers
5 views

deterministic limit of gaussian distribution

Let $a$ be a random variable over some set $A$, and let $\mathcal A \subseteq A$ be an event. Let $\mathcal E \subset \mathbb R^n$ be another event, and let $x_1, \dots, x_n$ be several Gaussian ...
0
votes
1answer
21 views

Probability Discrete Math

{1,2,3,4,5,6,7,8,9} What is the probability that the sum of any of these three numbers is odd? I know that I should use $ n \choose k $ somehow and I know that my professor used this as his equation: ...
0
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0answers
11 views

probability problem about Use the abstract properties of probability measures

Let $X$ be an arbitrary random variable on a countable probability space with probability measure $P$: Use the abstract properties of probability measures and expectations to prove the following: (a) ...
0
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0answers
8 views

looking for asymmetric probability distribution

In physics, quantities are sometimes measured with both an upper and lower error. For example, I might say that an object's mass is $m = 10^{+0.1}_{-0.2} \text{ kg}$. In my case, these arise from ...
0
votes
2answers
23 views

Preliminaries: Combinatorial Analysis [on hold]

There are 5 women and 7 men, how many different committees consisting of 2 women and 3 men can be formed? What if 2 of the men are feuding and refuse to be on the committee together?
0
votes
2answers
31 views

Number of necessary stickers to complete a sticker album

I have the following problem, and I was hoping you guys could help me solve it: Consider a set of $t$ unique, collectable stickers (that accounts for the universe of collectable stickers, i.e., ...
3
votes
5answers
94 views

$\sum\limits_{n=1}^\infty n(\frac{1}{2})^{n}$ [duplicate]

I am trying to find the expected value of the number of even numbers rolled before the first odd number when rolling a fair die until an odd number comes up. I arrived at $\sum\limits_{n=1}^\infty ...
0
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0answers
20 views

How to find the discrete probability vector given a transition probability matrix?

I have a transition probability matrix for the above Discrete Time Markov Chain I want to find the 'discrete probability vector' of this state space. My understanding is that the discrete ...