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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Probability, geometric distribution

What is the probability of $P(X<E(X))$ if $X$ has a geometric distribution such that $P(X=1)=0.25$. I found $E(X)=0.25$. I guess I should find $P(X=0)$, but I don't know how. I can only plug ...
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1answer
11 views

Question on Expected time using survival function

I am dealing with a problem that says: A machine requires the continual operation of two independent devices in order to keep functioning. It breaks down as soon as the first device stops ...
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0answers
11 views

Expected Value of the maximum of a set of random variables (not indep)

Suppose that we have a set of $n+1$ discrete random variables $X_{i}$ (for $0 \leq i \leq n$) that are identically distributed, but not independent, and for which we know the distribution (presumably ...
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0answers
32 views

Limit for the discovery of new maths? [on hold]

Just out of sheer curiosity, I question that will there be any limit to the discovery of new maths ? Would it eventually end! What is the probability of it ending?
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0answers
20 views

Homework help with Statistics and Probability

Luxury is a rental company that advertises that the average cost of a rental for undergraduate students is $\$525$ with a standard deviation of $\$95$. (Assume the rents are approximately normally ...
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3answers
27 views

Expected value of XY

I'm having trouble figuring out the expected value of xy. Random variables x and y are described by the joint PDF: $$f(x,y) = \begin{cases} K & \text{: if } x + y ≤ 1 , x > 0 , y > ...
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0answers
12 views

Chained conditional probability, lying and telling truth

Four witnesses A, B, C, D at a trial each speak the truth with probability 1/3 independently of each other. In their testimonies, A claimed that B denied that C declared that D lied. What is the ...
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0answers
16 views

Finite State Automaton and Probability

Draw a FSA and use it to determine probability of rolling HTT vs HHT. Probability to see H is p, while probability we see T is q, with p+q=1. I've been able to draw the FSA for this problem For ...
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2answers
14 views

Probability question (2 conditions)

Female smokers - 20 Male smokers - 40 Total smokers - 60 Non-smoking females - 70 Non-smoking males - 70 Total non-smokers - 140 Total females - 90 Total males - 110 Total - 200 If two people ...
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0answers
12 views

Probability function corresponding to these moment generating functions

Just a quick little practice question which I'm getting stumped on. Write down the density or probability function corresponding to the following moment generating functions: (i) $$M_1(t)= ...
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2answers
22 views

Rolling a balanced die 10 times

A balanced die is rolled 10 times by 5 different people. What is the probability that at least two people rolled exactly 4 twos, 3 fours and 3 sixes? So I know I'm looking for $P(X\ge 2)= ...
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1answer
10 views

Probability and Statistics random independent variables

I can't figure out how to determine if these variables are independent. Any help would be greatly appreciated. Random variables x and y are described by the PDF: $$f(x,y) = \begin{cases} k,& ...
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1answer
34 views

A good problem in probability

Two players play a series a games. In each game, each one of the two player wins a point (i.e. there is no draw), the first player have probability $p$, and the second have probability $q=1-p$, that ...
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16 views

Coffee machine exponential distribution

The amount of coffee a machine dispenses is an exponentially distributed random variable with mean 100cc. Suppose a cup will overflow if more than 120cc are dispensed. What is the probability that at ...
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0answers
14 views

show tha size biasing function is a pmf [on hold]

for the pmf P(i) for all i in Z = 0,1,2,3, ..., and a = sum from o to infinity of P(i) * i how can I show that L(i) = (i*P(i))/a is a pmf for i in Z I am aware of the properties of a pmf 1. P(i) >= ...
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2answers
25 views

expectation of maximum of infinte iid random variables

Recently I have considered the following question: for a sequence of i.i.d. random variables(maybe normal distribution), the expectation of the maximum of n such kind of variables is dependent on n, ...
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0answers
19 views

Find the probability that the second defective item is in the 7th round

Help is needed in finding the solution of the following problem:- Suppose 2 defected light bulbs are mixed with 10 good ones. The bulbs are tested one by one until both defected ones are found. What ...
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1answer
25 views

Need help with math and statistics. [duplicate]

The world population is ~7 billion Social Classes: Top .001% is ~70,000 Second .01% is ~700,000 Next .1% is ~7 million Rest 99.9% is ~6,993,000,000 (billion) The odds of 1 person in the ...
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1answer
42 views

Question about probability? World Population - (Question Revised)

The world population is ~7 billion Social Classes: x: Top .001% is ~70,000 y: Second .01% is ~700,000 z: Next .1% is ~7 million r: Rest 99.9% is ~6,993,000,000 (billion) p: population ...
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1answer
28 views

Probability error

I perform $N$ independent trials with $M$ successes. The probability of success is therefore $P=M/N$. Can I assign a sample-size-dependent error to the probability based only on this information? i.e. ...
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0answers
7 views

Probability of one node given all the others in a bayes network

For a bayes network which has $n$ nodes, $X_1, X_2, ... , X_n$. Is there any efficient way to calculate $P(X_i|X_1,X_2,...,X_{i-1},X_{i+1},...X_n)$, without constructing the full joint distribution?
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0answers
19 views

Choosing the integral limits for marginal distribution

I've been trying to understand the following: The distribution of two continuous random variables is given by $$f_{X,Y}(x,y)=\frac{3}{7}x\space\space 1\le x\le 2,0\le y\le x$$and $0$ otherwise. ...
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0answers
10 views

Showing that the series of random variables $X_n / n$ converges almost surely under some conditions

I'm working on a problem from Chow and Teicher's book on Probability Theory, page 123, #6(ii): If $X_n, n\geq 1$ are i.i.d., $\mathcal{L_1}$ r.v.s, then $\sum (X_n / n)$ converges a.c. if ...
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1answer
13 views

Probability Application | Sales Presentation Order

Heidi and Boyd are among 9 representatives making presentations at the annual sales meeting. The presentations are randomly ordered. Find the probability that Heidi is the first presenter and Boyd ...
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2answers
32 views

Probability rules help

The question is a die is rolled six times. What is the probability that $1,2,3,4,5,6$ will appear in that order? My question is what formula would you use to solve this because I know that when order ...
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1answer
25 views

Probability Application | Bridge Hand [on hold]

A Bridge Hand is made up of 13 cards from a deck of 52. Find the probabilities that a hand chosen at random contains the following. Only Hearts At least 3 Aces Exactly 2 Aces and Exactly 2 Kings 6 ...
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4answers
37 views

Basic Probability Question (Expected Value)

We are given a bag of marbles containing 6 blue marbles, 7 red marbles, and 5 yellow marbles. We select 4 marbles without replacement. How can we calculate the expected value of the number of blue, ...
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3answers
144 views

distribution of $X^2 + Y^2$

Suppose $X$ and $Y$ are independent uniform distributions between $(0,1)$. What is the distribution of $X^2 + Y^2$? I derived that the pdf of $X^2$ is $\frac{1}{2\sqrt{x}}$ for $0\leq x \leq 1$. How ...
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1answer
47 views

Determine the probability that a randomly selected integer is divisible by one of several integers.

If you choose an element x uniformly at random from the set {1,2,...,100}, what is the probability that x is divisible by 4 or 5? Can someone explain why the answer is 2/5 please, thanks.
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0answers
31 views

how can prove this statement?

According definition of Kullback–Leibler divergence, we have: $"k[f|g]=\int_{}^{} f(x)\log \frac{f(x)}{g(x)}\mathrm dx"$. Now How can I prove this statement:$$k[f|g]=k[f|w]k[w|g].$$ Thanks in advance. ...
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1answer
23 views

How to represent the notion that “at least one event occured”

Given two events, A and B, if it is the case that "at least one of the events occurred", I have seen it written that we can identify that probability as $$pr(A \cup B)$$ I'm struggling to understand ...
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1answer
42 views

Asymptotics of sum of Binomial Coefficients (Binomial distribution) - Poisson approximation?

Let $$f(n):=\sum_{i=k}^n {n \choose i } p^i (1-p)^{n-i}$$ where $k\geq 2$ is a fixed Parameter and $p=p(n) \in (0,1]$ depends on $n$ where $np\leq 1$. We consider $n \rightarrow \infty$. I've found ...
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1answer
24 views

Solutions to a stochastic birth-death-immigration process

A population is undergoing a birth-death-immigration process. That is, the population size can increase by virtue of birth and immigration, and can decrease by virtue of death. The birth rate is ...
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1answer
28 views

probility, placing balls, covariance

Can you please help to see where I did wrong? There are 10 balls, and each ball to be place in bin 1 and bin 2. Each ball is placed indepedently. Let X be the number of balls in bin 1 and Y be the ...
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1answer
18 views

Theoretical Probability

Brady spun the arrow 100 times on the spinner. The arrow landed on the section "P" 18 times. How many more times should the arrow have landed on the section labeled "P" to match the theoretical ...
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1answer
21 views

Clustering And Distribution in An Unfair Coin Flip

A coin is biased such that lands heads up 40% of the time and tails the other 60% of the time. You flip this coin eight times and three of those flips land heads up. If the greatest clustering is ...
2
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1answer
15 views

probability, transformation on Random Variable

This is a more general question about the transformation of a random variable. Say X is given as a certain distribution, and Y=g(X). If it asks to compute the pdf of Y, I am having trouble to ...
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1answer
19 views

expected size of a special set of random points in the unit square

Today I came up with this fun problem, but I'm having a hard time to solve it completely myself. The question is the following: Let's generate n random points ...
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2answers
32 views

Probability Urn Problem

An urn contains 3 red balls and 6 blue balls. Two balls are drawn without replacement and the second is found to be red. What is the probability that the first ball was also red? I thought it would ...
0
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1answer
26 views

Calcuate the test statistic

I am facing a little problem is this question. Can somebody please help e here A sample of 500 drivers was asked whether or not they speed while driving. The following table gives a two-way ...
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1answer
39 views

Confusion about an algorithm making a choice between two options, with probabilities.

I am totally puzzled at grasping the meaning of "we move to B with probability P1 OR we move to C with probability P2" in the following scenario. A,B,C are points in a 64-dimensional space. Reading ...
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1answer
44 views

probability of sequence of integers

Suppose you have numbers from 1 to 10. You can choose four of them but the contiguous numbers should have an absolute difference greater than 1. For example, you can choose $$ 1-3-6-10$$ $$ 4-2-5-1$$ ...
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1answer
22 views

probability of drivers wearign seatbelts

if 80% of Ca drivers wear seat belts and three drivers are pulled over what is the probability that all three will be wearing their seat belt
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1answer
36 views

The critical value

I am facing a little problem is this question. Can somebody please help e here A sample of 500 drivers was asked whether or not they speed while driving. The following table gives a two-way ...
0
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2answers
32 views

standard deviation

It has been reported that household in the west spend an annual average of \$6050 for groceries.Assume a normal distrubition with a standard deviation of \$1500. (a) What is the probability that a ...
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2answers
22 views

rolling dice 6 times, outcomes showing of 2 sixes

If 6 dices are rolled, in how many ways will exactly 2 sixes show up? I was thinking that it would be 6*6*5*5*5*5, am I right?
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1answer
25 views

Probability math problem. [on hold]

Certain data obtained from a study of a group of 1000 subscribers to a certain magazine relating to their sex, marital status, and education were reported as follows: 312 males, 470 married, 525 ...
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3answers
36 views

The Objectivity of Statistical Testing

I have a very generic question about applied statistics. Suppose, to make things simple, we have a biased coin with probability $p$ of landing heads. We want to determine if our coin is truly fair - ...
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1answer
30 views

Continuous Probability Density Function

The problem is: Verify that the function p: [0,2] [0,1] given by p(X) = {X, if 0 < X < 1 2 - X, if 1 < X< 2 is a ...