1
vote
2answers
38 views

How do I transform an r.v. using the floor function? (exponential distribution)

Just had a bash at this question for my Intro to Maths Stats module...I got to the end with a probability density function rather than a probability mass function, namely $f_Y(y) = \lambda a ...
0
votes
2answers
32 views

What is the 'growth constant'?

I'm looking into the formula of growth, namely $$N= N_0 e^{kt}$$ where $k$ is the 'growth constant'. What is the growth constant and how do I find it? I'm looking at a bug that has on average 1,67 ...
1
vote
1answer
54 views

What's the MLE of lambda for $f(x)= \frac{1}{λ}\exp{\frac{−x}{λ}}$?

What's the MLE of $\lambda$ for $$f(x)= \frac{1}{λ}\exp\left({\frac{−x}{λ}}\right)$$ Values of x are 5,7,9,3,6,8 Is it just the mean of $x$? Thanks.
0
votes
1answer
34 views

variance of minimum of squared exponential random variable

Given $Y_1 $ to $Y_n$ are exponential r.v's with mean $\theta$ find $\operatorname{var}[\min(Y^2 )]$ with the help of gamma distribution. attempt: $\min(Y) $ is exponential with $(\text{mean} = ...
0
votes
2answers
88 views

Mean and Variance of exponential function

Given this function with j and k as unknown parameters. What is the expression of Variance and Mean of this exponential function? $$f_{j,k}(y)=\frac{\sqrt{j}}{\sqrt{2 ...
0
votes
1answer
67 views

Show that a statistical model belongs to exponential family

I have this statistical model: $$f_{j,k}(y)=\frac{\sqrt{j}}{\sqrt{2 \pi}}e^{\sqrt{jk}}y^{-\frac{1}{2}} \text{exp}\left( -\frac{1}{2} (j y + \frac{k}{y}) \right) \quad \quad y>0$$ In this case the ...
1
vote
0answers
299 views

Exponential integral approximation

I have an equation that contain exponential integral of the form: $$ \begin{equation} E_k\left(\frac{a+b ~x}{c}\right) \end{equation} $$ Where $k\geq 0$ ($k=0,1,2,...$), $a$, $b$, and $c$ are ...
1
vote
1answer
1k views

Derive the PDF of the log-normal distribution?

If $X \sim N(0,1)$ and $Y = e^X$, find the PDF of $Y$ using the two methods: (i) Find the CDF of of $Y$ and then differentiate. Use the notation $\Phi(x)$ and $\phi(x)$ for the CDF and PDF of $X$ ...
0
votes
1answer
203 views

Expected value of minimum of exponentials

I am not sure of the following. I have $(i-1)$ exponential random variables with rates $\theta$ and $\mu$ and I want the expected value that the particular $\mu$ random variable is the minimum. Think ...
1
vote
1answer
62 views

Non-trivial solution for $2*a^k = b^k + c^k$

I have a data set where I want its median to be the arithmetic average of maximum and minimum by multiplying every value with a factor $k$ and then applying the exponential function. This leads to the ...
2
votes
1answer
62 views

How do I find the mean with this exponential?

p(y) = c/y^4 I need to find the "mean & variance" of this exponential density function. Some pointers or thoughts that would explain would be most helpful. ...
2
votes
2answers
393 views

Exponential Distribution MLE

The lifetime of a type of component has an exponential distribution with rate λ per hour. Ten of these components were tested but the only recorded results were that 3 components had failed within 100 ...
2
votes
1answer
541 views

Logistic function passing through two points AND the origin?

I had recently asked the question: http://math.stackexchange.com/q/8213/2916 which received a very helpful answer. However, I'd like to ask your help again as the formulation of the problem has ...