283,212 reputation
21249515
bio website
location
age
visits member for 3 years, 7 months
seen 8 mins ago

2h
comment Probability: Distinguishable vs Indistinguishable
Your calculation and reasoning are correct. For many probability problems involving indistinguishables, it is useful to imagine that the objects have ID numbers written on them, if you like in invisible ink. Of course the probability does not change, but counting is more likely to be correct.
2h
comment Detailed explanation of the derivation of the expected number of coin tosses
The issue is taken account of, though without detail, in the first sentence of that answer: we assert that the expectation exists.
2h
comment find the volume for the region
Presumably we are rotating a certain region about some line. The region has not been described precisely, nor has the line.
2h
reviewed Leave Open Distance, Speed and Time problem
2h
reviewed Leave Open Age Calculations using cubed roots
2h
answered Solve recursion with constant added
3h
reviewed No Action Needed Mapping set of integers to irrational numbers.
3h
reviewed Leave Open Find the distance
3h
comment discrete random variable
The image description failed, so I do not know the distribution of $X$. For the mean, variance of $Y$, use the fact that $E(aX+b)=aE(X)+b$ and $\text{Var}(aX+b)=a^2\text{Var}(X)$. By the way, it is highly unlikely that $\text{Var}(X)=0$.
3h
comment Detailed explanation of the derivation of the expected number of coin tosses
The standard formula for the expectation of a discrete random variable does have the shape you quote. But that does not mean that using the formula is the only way to compute expectation. In my solution, conditioning (on the results of the first few tosses) was used. There are other ways of finding expectation that bypass finding the probabilities $p_i$.
3h
reviewed Reopen Deriving the Pareto Distribution from an Exponential Distribution
3h
reviewed Looks OK Find all complex and real roots of higher degree polynomials, given one root
3h
reviewed No Action Needed How to do you compute the probability a record occurring in a sequence of independent experiments?
3h
revised Find all complex and real roots of higher degree polynomials, given one root
added 220 characters in body
3h
answered Find all complex and real roots of higher degree polynomials, given one root
3h
reviewed No Action Needed If $A=5r^2$ and $\frac{dA}{du}=2$, what is $\frac{dr}{du}$
3h
reviewed Leave Open Abstract algebra: equivalence relations on vector spaces
3h
comment Exponential random variable with mean 1/gamma
Your book/notes have the density function of a gamma distribution. The integral from $0$ to $\infty$ of this density function is $1$. It is that fact that you are intended to use, to evaluate your integral. Of course you can evaluate it in other ways, such as repeated integration by parts.
3h
reviewed Leave Open Probability replacement
4h
comment finding solutions by factoring
Maybe one should add that $u$ and $v$ should be chosen to be both even, and possibly negative.