Calculus and Above

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Let X1,...,Xn be i.i.d. random variables with p.d.f. f(x;θ)=
Let X1,...,Xn be i.i.d. random variables with p.d.f. f(x;θ)= 1 exp􏰅−x􏰆I(x>0), where θ∈Θ=(0,∞). θθ… read more
MunishK
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Ff: R→Risafunction,thenwewritelimx→af(x)=Ltomean: ∀ε > 0 ∃δ
ff: R→Risafunction,thenwewritelimx→af(x)=Ltomean: ∀ε > 0 ∃δ > 0 ∀x ( (0 < |x − a| < δ) → (|f (x) − L| < ε) ). (The universe for all variables is R.) a) Find the negation of the definiti… read more
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The joint pdf of a bivariate random variable (X,Y) is given
The joint pdf of a bivariate random variable (X,Y) is given by: f(x,y) = ck for 0… read more
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Let L be the number you computed earlier. The joint PMF of
Let L be the number you computed earlier. The joint PMF of random variables X and Y is given by: P(n,k) = [(L^n)(e^-L)]/n!(C(L,k))(p^k)(1-p)^(L-k) for n = 0,1,2,... and 0<= k <= L and 0 otherwis… read more
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Let X and Y be independent random variables. The pdfs of X
Let X and Y be independent random variables. The pdfs of X and Y are: fX(x) = e−x for x>0 fY(y) = e−y for y>0. FindP(X+Y >1).… read more
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I have two questions in advanced stochastic process
I have two questions in advanced stochastic process assignment nee help … read more
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Doctoral Degree
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I am preparing for a probability theory test and I am having
I am preparing for a probability theory test and I am having problems with MGF's these are some examples from previous exams which I would like solutions for along with explanations to help me study. … read more
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1. (a) Use the definition of moment generating functions to
1. (a) Use the definition of moment generating functions to show that if MX(t) is the mgf of a continuous random variable X, then if Y = (X+a)/b, MY (t) = e^(a/b)t MX(t/b) ￼￼ (b) Choose appropriate co… read more
Expert
1. The cashier service time at the local branch of the Rivertown
1. The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time: Is between 2 and 4 minu… read more
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A random variable X has the probability density f(x):=2axe^-(ax^2)
A random variable X has the probability density f(x):=2axe^-(ax^2) for x>0 and 0 otherwise where a>0 is a parameter. Show that E[X] = 1/2 sqrt(pi/a).… read more
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1. Let events An increase to A. Find A and show P(An ) -> P(A).
1. Let events An increase to A. Find A and show P(An ) -> P(A). Show the same thing in the decreasing case. Use these results to show that a df F is right continuous, F(oo)=1, F(-oo)=0. 2. Let X be… read more
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1) A point is generated at random in the plane according to
1) A point is generated at random in the plane according to the following polar scheme. A radius R is chosen, where the distribution of R^2 is X^2 with 2 degrees of freedom. Independently, an angle θ … read more
Dr Arthur Rubin
Doctoral Degree
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The Pareto distribution, with parameters α and β, has pdf
The Pareto distribution, with parameters α and β, has pdf f(x)=(βα^β)/x^(β+1) ,α0. a)Verify that f(x) is a pdf. b) Derive the mean and variance of the distribution. c) Prove that variance does not exi… read more
rajeevanpillai
Master's Degree
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Let X1,X2,...,Xn represent a random sample from a population
Attachment: 2012-04-24_132012_img.pdf Let X1,X2,...,Xn represent a random sample from a population with a gamma(2,b) distribution, i.e. its probability density function is given by f(x;b) =(xe^(-x/b))… read more
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Let Xi,i=1,2,...,n be a random sample from the distribution
Let Xi,i=1,2,...,n be a random sample from the distribution having pdf f(x,Q1,Q2)=(1/Q2)e^(-(x-Q1)/Q2) , Q1<= X < +infinity , -infinity < Q1 0. Find the Maximum Likelihood Estimators (MLEs) … read more
rajeevanpillai
Master's Degree
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Give a method for generating a random variable having distribution
Give a method for generating a random variable having distribution function F (x) = 1 − exp(−αx^β ), 0 < x < ∞. A random variable having such a distribution is said to be a Weibull random variab… read more
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Use the inverse transform method to generate a random variable
Use the inverse transform method to generate a random variable X having the distribution Pr(X=i)= 1/[i(i+1)] , i=1,2,.... Write the algorithm, but you don't need to implement it. Hint: Determine the d… read more
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Master's Degree
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Give a method for generating a random variable having distribution
Give a method for generating a random variable having distribution function F (x) = 1 − exp(−αx^β ), 0 < x < ∞. A random variable having such a distribution is said to be a Weibull random variab… read more
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Doctoral Degree
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