Tagged Questions

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What happens to the sum of Bernouilli RVs divided by $\sqrt(n)$

Suppose I have $$S=\frac {\sum_1^nX_i} {\sqrt(n)}$$ where $X_i$ is Bernouilli($p$) and $n$ goes to infinity. It doesn't look like it's approximately normal (the CLT doesn't apply since it's not ...
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Which of the following distributions could satisfy the law of large numbers?

I am working on the following question: A random variable Z is a choice of two RVs: X and Y, selected randomly, i.e., some $Z$ values were "originally" $X$'s, and the others were $Y$'s. For a ...
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Find the probability that the average of X and Z is greater than Y. Where X, Z, and Y are normal RVs.

Here is the exact statement: Suppose X,Y , and Z are independent random variables. X is a normal random variable with mean 5 and variance 16, Y is a normal random variable with mean 7 and variance ...
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Bessel's inequality for expected value

Let $X_1, X_2,\ldots$ be independent random variables with expected value $\mathbb{E}[X_i]=0$ and variance $V[X_i]=1$. Let $Y$ be another random variable, such that $\mathbb{E}[Y^2] < \infty$. I ...
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Bob has a 98% chance of making any freethrow. He throws until he misses. Determine the chance that: a) he misses for the first time on the 9th or 10th throw b) he misses for the first time on the ...
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Probability Distribution Question

On a football team there are 7 quarterbacks and 6 linemen. Coach selects 5 players. a) Determine the probability that he selects only 1 quarterback b) Determine the probability that he selects more ...
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Probability Distributions Question

A lottery corporation sells 100 000 tickets at \$3.00 per ticket. If the lottery has 2 first prizes worth \$20,000 each, 4 second prizes worth \$5000 each and 10 third prizes worth$500 each, ...
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Applying transition matrix to a probability vector seems to ruin its normalization

I had a little bit about stochastic processes during my "Statistical Physics" course and on my exam I got a problem with a Markov chain. My solution seems to be without computational mistakes (checked ...
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Three married couples have bought $6$ seats in a row for a concert. How many ways can they be seated if no man sits next to his wife. I have worked through this problem and have got the correct ...
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Finding the expected value of a random variable

Let: $$f(x) = \begin{cases} k(\frac23)^x, & \text{if }x \in \{1, 2, 3,\ldots\} \\[2ex] 0 & \text{elsewhere}\end{cases}$$ Find $k$: Because $x$ is countable, it is discrete. So, a $\sum$ is ...
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A machine has $9$ switches. Each switch has $3$ positions. How many different settings are possible?

A machine has $9$ switches. Each switch has $3$ positions. $(1)$ How many different settings are possible? Each switch has $3$ different settings and we have $9$ total. So, $3^9=19,683$ Now, the ...
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Probability a 9-digit number has the digits 2,4, and 6 next to each other.

The integers $1,2,3,....,9$ are arraned (at random) in a row, resulting in a $9$-digit integer (without replacement). What is the probability that: The result is even? $\frac49$ or $\frac{4(8!)}{9!}$ ...
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probability problem - expectation

A tourist wants to visit four cities: A, B, C and D. First he chooses one at random. If he chooses A he then randomly chooses among B, C and D. If he chooses B then he randomly chooses among A, C, D. ...