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 ...
0
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0answers
34 views
Does asymptotic normality imply convergenc in probability
Is that true that if $X_n$ is $AN(u,\sigma_n)$ ,then $X_n$ converges to $u$ in probability if and only if $\sigma_n \rightarrow,n\rightarrow\infty$? If it is true , then how to prove it ? Thanks in ...
0
votes
1answer
66 views
Probability of red-flowering independent of other plants
According to genetic theory, plants of a particular species have a $25%$ chance of being red-flowering, independently of other plants. Find the normal approximation to the chance that among $10,000$ ...
0
votes
1answer
123 views
Finding probability that a person gets $7$ when rolling a pair of dice
*I STILL DON'T GET THE ANSWERS PROVIDED. PLEASE HELP!
In a game, the participant rolls a pair of dice. If the result is a $7$, he wins. If the outcome is a number $n$ different from $7$, he continues ...
0
votes
1answer
53 views
Probability 2 people have a birthday in the same month out of 7
What is the probability that 2 people in the group have a birthday in the same month out of 7 people?
I know the answers 88.85% however I want to know how to work it out using factorials instead of ...
3
votes
1answer
94 views
Truchet tiles on a flattened cube
We randomly place copies of the tiles into faces of the flattened cube. 1.Find the probability that the circular arcs on the Truchet tiles will form one loop, two loops, three loops and four loops? ...
0
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0answers
20 views
finding the number of square we get when randomly put patterns into a given table [duplicate]
the image of the three tile patterns is here. [http://imageshack.us/photo/my-images/211/solpd.jpg/]
1
vote
1answer
38 views
Placing beads on a necklace, 7 colours. How many can be made
Dude wants to make a necklace with 7 beads, each a diffrent color.
(red, orange, yellow, blue, green, indigo, violet) placed on a chain that is then closed
to form a circle. How many different ...
-1
votes
0answers
160 views
Probability of random generator draw at random with replecement
A random number generator draws at random with replacement from the digits $\{0,\dots,9\}$. In $5000$ draws, the chance that the digit $0$ appears fewer than $495$ times is closest to: $0.25$, $0.3$, ...
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0answers
15 views
Naive Bayesian Classifier for Object with Variable attributes
Let say our objects are connected graphs. They are to be classified into two categories, say A and B. However, for our purpose attributes for each graph is equal to the number of vertex of the graph ...
1
vote
1answer
32 views
Upper bound on a probability generating function with a finite first moment
If $X$ is discrete random variable taking values in non-negative integers $\{0,1,\ldots\}$, its probability generating function is defined as follows:
$$G(z)=\mathbb{E}(z^X)=\sum_{x=0}^\infty ...
0
votes
1answer
45 views
correlation between a discrete uniform and a continuous uniform rvs
Suppose X and U are independent random variables with
P(X = k) =$\frac 1 {N+1}$, k= 0, 1, 2, . . . ,N,
and U having a uniform distribution on [0, 1]. Let Y = X + U.
a) For y ∈ R, find P(Y ≤ y).
b) ...
12
votes
2answers
188 views
A card game with no decisions
A friend showed me a mindless card game he plays, in which the initial state of the deck completely determines whether he wins or loses. The game is played as follows:
Shuffle a standard $52$ card ...
0
votes
1answer
376 views
Probaility of test score of a true and false independently of other questions guessing at random
A true-false test consists of 20 questions, each of which has one correct answer: true, or false. One point is awarded for every correct answer, but one point is taken off for each wrong answer. ...
2
votes
2answers
20 views
Probability Question for a “percent success” event.
If an event has an 85% chance of success, and you attempt the event 4 times, what are your chances of 3 or more successes?
If these were coin flips, I know there are $2^4$ possibilities. Of these ...
3
votes
2answers
22 views
Distribution of a group of people and a subset of them
Given $n$ people, each has probability $v$ of having a virus. Of those with the virus, they are hospitalized with probability $p$. Independently of having the virus, any of the $n$ people may be ...
3
votes
3answers
46 views
Probability/Combinatorics Problem - Old Maid Cards
A special deck of Old Maid cards consist of 25 pairs and a single old maid card. All 51 cards evenly between you and two other players – 17 cards for each player.
(a) how many different ...
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0answers
37 views
Random Walk, Coin flip game [closed]
Consider the coin flipping game, where player $A$ pays $B$ \$1 for each Heads, and vice versa for each Tails. (The coin is unbiased here.) Let $X_1$ be the random variable recording the first time ...
1
vote
0answers
42 views
Calculating a probability
Given $m\cdot e$ balls, $b$ of which are black (suppose the rest are white balls). Randomly put the balls into $m$ baskets, with $e$ balls in each basket. What is the probability of the event that ...
0
votes
1answer
17 views
Dose X converges in probability to Y converges in probability to a constant z implies X converges in probability to z
Suppose we have $\frac{1}{n}\sum_j^n X_{ij}$ converges in probability to $Y_i$ and $\frac{1}{n}\sum_y^n Y_{j}$ converges in probability to a constant $z$, where $Y_i$ is not the expectation value of ...
1
vote
2answers
53 views
A probability question: a building and an elevator.
Suppose that 7 people waiting for an elevator in a building with 14 flours.
Q: What is the probability that every person get out in different flour?
My attempt:
There is $14 \cdot 13 \cdot 12 \cdot ...
0
votes
2answers
29 views
Probability using C(n,k) 1
A family of five children is known to have at least two girls.What is the probability of this family having exactly four girls?
0
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0answers
21 views
C.D.F. of a maximum depending on two random variables and an absolute value
If $X$ and $Y$ are exponential and independent random variables with parameters $\lambda$ and $\mu$ respectively, find the C.D.F. $F_U(u)$ of $U = max(0, X-Y)$, determine if U is continuous, and ...
0
votes
1answer
36 views
Lifetime of a light bulb
Light bulbs average 800 hours of life (here the life time of a bulb follows an $\exp(1/800)$ distribution). Buy 1000 bulbs. Find the probability that the fourth bulb has gone out before 3 hours have ...
0
votes
0answers
13 views
fGn asymptotic claim correlation
Let $(X_{i})$ be the fractional Gaussian noise for $H\in(0,1)$.
Since it is stationary $\mathbb{E}(X_{i}X_{j})$ only depends on $|j-i|$.
How can I prove for $\rho(|j-i|)=\mathbb{E}(X_{i}X_{j})$ that ...
2
votes
2answers
34 views
Finding probability's distribution and calculation
I am trying to understand what is the implied distribution of the following problem:
A student asks for help from the professor 2 times per test on average.
the student took 5 different test
a) what ...
1
vote
0answers
19 views
Dealing with conditional probability
A programmer's programs are correct or buggy with equal probability 1/2, independently. Three of his programs are randomly selected. Assume that one of the three is inspected at random, what is the P ...
1
vote
2answers
31 views
Number of length-five words
How many length-five words can be written using two A's, two T's and one E?
Why is it not $\binom5 2 \times\binom 5 2 \times \binom 5 1$?
Is it $ \binom 5 3 = 10$?
1
vote
1answer
36 views
Finding a probability distribution given the moment generating function
The $n$-th moment ($n \geq 1$) of a random variable $X$ is given by: $m_n = \frac{2^n}{n+1}$. Find the probability distribution of $X$.
Here's my attempt at a solution: I expand the moment generating ...
0
votes
1answer
26 views
Probability a function has real zeros
What is the probability that the function f(x) = x^2 + rx + s has real zeros when r and s are real numbers between 0 and 9 inclusive?
1
vote
1answer
39 views
Moment generating function of two non-independent Brownian increments
I am writing to ask if it is possible to get closed-form solution to the expression to the following expression:
$\mathbb{E}[e^{\sigma^2(W_t-W_u)(W_s-W_u)}]$ where $W$ is a standard Brownian motion, ...
2
votes
0answers
27 views
Expectation of the area [duplicate]
Choose randomly three points in the unit square $D=\{(x,y)\mid 0\leq x, y\leq 1\}$, is it possible to calculate the expectation of the area of the triangle with the three points as vertexes? (Of ...
4
votes
0answers
36 views
Different Perspectives of Multinomial Theorem & Partitions
There are 2 important interpretations of the multinomial theorem and coefficients.
1: Determining the number of ordered strings that can be formed using a set of letters. For example, with 1 m, 4 ...
1
vote
0answers
24 views
Density function of the sum of uniformly distributed random variables [duplicate]
Suppose we choose independently two numbers $X$ and $Y$ , at random,
from the interval $[0,1]$ with uniform probability density. What is the
density of their sum $Z = X + Y$ ?
I know that the ...
1
vote
1answer
53 views
What is the probability that, given the smallest of 50 random integers(>0), it will be the smallest of 50 other random integers (one being itself)?
More generally, if an array of random integers (size N), and another array of random integers (size M), "overlap" by R numbers (have them in common):
What is the chance that the smallest of one is the ...
3
votes
2answers
38 views
Probability of selecting correct answer in 15 out of 25 exercises with 0.25 chance
There are 25 exercises, each one consists of answers: a, b, c, d and only one answer is correct. My question is what is the probability of selecting correct answer in 15 out of 25 exercises.
My idea: ...
0
votes
1answer
24 views
Estimating a probability with converging moments
Let me rephrase my question.
If you look at the random variable $X$ which simply picks a random integer between $1$ and $N$ (distributed uniformly) and now look at the inequality
$$
t^k \cdot ...
0
votes
0answers
31 views
Probability: How many ways can be ordered.
A cafe serves 6 kinds of soups, 5 kinds of salads, and 20 kinds of entrees.
Q: How many ways can I order a salad or a soup?
there are 5 + 6 = 11 ways.
but I'm confused whether I need to consider ...
0
votes
2answers
47 views
probability based on geometry
A rectangle is drawn where the lengths of the sides are chosen randomly
from [0, 10] and independently of one another. Find the probability
that the length of its diagonal is smaller than or equal to ...
1
vote
1answer
28 views
Chernoff bound proof using Markov
Does anyone familiar with the following format of Chernoff bound:
$$
Pr\left(\frac{1}{n}\sum\limits_{i=1}^n X_i \gt T\right ) \le \inf_{\gamma \gt 0}{\left ( \frac{E[e^{\gamma X_i}]}{e^{\gamma T}} ...
0
votes
0answers
15 views
Joint Probability in terms of Spectral Matrix
Given a multivariate time series ${\bf x}(t)$ with known spectral matrix ${\bf S}(f)$, how would I be able to display the likelihood function
$$p_{{\bf x}}({\bf x}(1),{\bf x}(2) \dots {\bf x}(N))$$
in ...
0
votes
3answers
44 views
What is the probability of the roulette ball landing in a black slot?
There have been $15$ consecutive red. What is the probability of the roulette ball landing in a black slot next?
What I did --
probability of landing on red is $\dfrac{18}{38}$
so there have ...
2
votes
1answer
146 views
Another hat problem
A finite number of prisoners, after being given their hats (black or white), are able to see one another but themselves, and then they are ordered to jot down their guess on the color of their own ...
0
votes
1answer
41 views
Algebra involving expected values
If $C = A + B$ (hence $\mathbb{E}[C]$ = $\mathbb{E}[A]$ + $\mathbb{E}[B]$) and $p(A = a) = 1$, are the following true?
$\mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2]$
$\mathbb{E}[C^3] = ...
0
votes
3answers
60 views
Revised GRE Math Probability section
The table shows the distribution of a group of $40$ college students by gender and class
$$
\begin{array}{c|lcr}
& \text{Sophomores} & \text{Juniors} & \text{Seniors} \\
\hline
...
0
votes
1answer
27 views
Probability & Statistics
You and a friend play a game in which the winner is the first player who has
7 or more points and is 2 points ahead of the other player. Note that game
involves rounds of play, and the winner gains ...
0
votes
1answer
91 views
Covariance and Correlation
Suppose there were m married couples, but d of these 2m people have died. Regard the d deaths as striking the 2m people at random. Let X be the number of surviving couples.
Find:
a) E(X)
b) Var(X)
...
0
votes
1answer
36 views
Correlation of Indicator Variables
Show that for indicator random variables IA and IB of Events A and B:
Corr(IA, IB) = Corr(IAc, IBc) = -Corr(IA, IBc) = -Corr(IAc, IB)
Deduce that if A and B are positively dependent, then so are Ac ...
0
votes
0answers
39 views
Invariance of the correlation coefficient under linear transformations
Show that for arbitrary random variables X and Y, and constants a ,b ,c ,d with a and c nonzero, Corr(a*X+b, c*Y+d) = Corr(X,Y) if a and c have the same sign
= -Corr(X,Y) if a and c have opposite ...
-3
votes
1answer
115 views
What is the probability that both the fuses are defective? [closed]
A box contains $20$ fuses of which $5$ are defective. If $2$ fuses are chosen together at random, what is the probability that both the fuses are defective?
0
votes
0answers
21 views
Conditional Probability (twice applied)
I am trying to better visualize why:
$$P(A|B,C) = [P(B|A,C)P(A|C)]/P(B|C)$$
I know we can get this by doing:
$$ \,\,\,(1)\, P(A|B,C) = P(A,B|C)/P(B|C) \\ (2)\,P(A,B|C) = P(B|A,C)P(A|C)$$
I can ...
