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Jul
8
comment Probability Question involving Probability Mass Function/Random Variables
You've already determined that $P(K=k)=\binom{n}{k}p^k(1-p)^{n-k}$. Part (b) is asking you to solve for $n$ such that $P(K\geq1)\geq0.95$. Another way to look at this is that the probability of not receiving the message correctly at all should be less than 5%: $P(K=0)=(1-p)^{n}\leq0.05$.
May
28
answered If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$, then prove that $P(x) \cdot Q(x) = 0$ has at least two real roots?
Mar
25
awarded  Critic
Nov
16
comment Lottery probability question…
Second place needs to capture exactly five of the six numbers. How many ways can this be done? The denominator remains the same: there are still $\binom{59}{6}$ ways to draw six numbers from 59. However, the numerator should count the number of ways you may draw five numbers from the winning six and one number from the remaining 53 numbers.
May
15
awarded  Caucus
Feb
24
comment Given $x(t) = u(t)$ and $h(t) = \cos(\pi t)u(t)$, how do we find the response $y(t)$?
I don't see why the integral isn't $\int_{0}^{\infty}cos(\pi\tau)u(\tau)u(t-\tau)d\tau$.
Nov
7
answered Poisson Distribution for Consecutive Figures
Nov
2
comment Solve Ax = b where b are labels instead of values
@locke14 I misunderstood the question. My response was for $A$ having these entries, not $b$.
Nov
2
comment Solve Ax = b where b are labels instead of values
Usually with categorical variables, one category is chosen as a baseline and all others are assigned their own indicator variable in the regression. For example, if the original variable represents weight and the categories are "low", "medium" and "high", we may choose "medium" as the baseline and create two other variables named "isLow" and "isHigh". If a person has "medium" weight, isLow and isHigh will both be zero. If a person has "low" weight, isLow will be one and isHigh will be zero. If a person has "high" weight, isLow will be zero and isHigh will be one.
Oct
30
comment Process for $(k+1)^3$?
@wj32 Ah. That makes sense.
Oct
30
comment Process for $(k+1)^3$?
You don't mention the binomial theorem anywhere in your question.
Oct
30
comment Process for $(k+1)^3$?
Look into the binomial theorem.
Oct
28
comment Puzzle on Ranks
The computation is correct. This is a good way of thinking about the problem though.
Oct
26
accepted Help Needed: Partial Derivative Identity/Chain Rule
Oct
26
comment Formulas for the multivariate Gaussian function?
If you convert the density function to use the actual elements of $x$ and $\Sigma$ rather than the matrix equivalents, taking derivatives will become more clear.
Oct
17
comment Calculating Variance of a binomial distribution using the standard formula $E(X^2) - \mu^2$
Yes, that is correct.
Oct
17
revised Calculating Variance of a binomial distribution using the standard formula $E(X^2) - \mu^2$
added 186 characters in body
Oct
17
answered Calculating Variance of a binomial distribution using the standard formula $E(X^2) - \mu^2$
Oct
17
comment Calculating Variance of a binomial distribution using the standard formula $E(X^2) - \mu^2$
I think you mean $Var(X)=E(X^2)-\mu^2$.
Oct
15
comment Approximate probability mass function into normal distribution
The normal distribution is characterized by its two parameters: its mean and variance. Find the mean and variance of your data ($\bar{x}$ and $s_x^2$, respectively) and plug those in to the normal density function.