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Questions (19)
Consider the Vasicek model for the short rate
dr(t)=(b−ar(t))dt+γdW1(t) and the Black-Scholes-Merton model for a stock S
4 answers
668 views
The price of a US stock is given by
dS(t)/S(t)=μdt+σdW1(t) The exchange rate Dollar/Euro is given by dQ(t)/Q(t)=βdt+δdW2(t)
3 answers
898 views
Consider a Black-Scholes-Merton model with r=0.1, T=0.5 years, S(0)=100. Suppose the Black-Scholes price of the digital option
4 answers
722 views
Consider the Black-Scholes-Merton model for two stocks:
dS1(t)=0.1S1(t)dt+0.2S1(t)dW1(t) dS2(t)=0.05S2(t)dt+0.1S2(t)dW2(t)
3 answers
952 views
Suppose you have written a derivative that pays the squared value of the stock price at maturity T=1; that is, it pays S2(1).
3 answers
571 views
Assume that the future dividends on a given stock S are known, and denote their discounted value at the present time t by
2 answers
595 views
A default-free coupon bond maturing in 6 months, that pays a coupon of 2.00 after 3 months and makes a final payment of 102.00
4 answers
1,143 views
At time zero you enter a long position in a forward contract on 1 share of the stock XYZ at the forward price of 10.00.
2 answers
783 views
Problem 3: Checking the Markov property
For each one of the following definitions of the state Xk at time k (for k=1,2,…),
5 answers
3,787 views
Problem 2: Oscar's running shoes
Oscar goes for a run each morning. When he leaves his house for his run, he is equally likely to
5 answers
4,993 views
Tossing a pair of coins
We have a white coin, for which P(Heads)=0.4 and a black coin for which P(Heads)=0.6. The flips of the
5 answers
1,602 views
The PDF of exp(X)
Let X be a random variable with PDF f_X. Find the PDF of the random variable Y=e^X for each of the following
3 answers
1,095 views
FUNCTIONS OF A STANDARD NORMAL
The random variable X has a standard normal distribution. Find the PDF of the random variable Y,
4 answers
3,590 views
Exercise: Sections of a class
A class consists of three sections with 10 students each. The mean quiz scores in each section were
10 answers
3,149 views
Let K be a discrete random variable with PMF
pK(k)=⎧⎩⎨⎪⎪1/3,2/3,0if k=1,if k=2,otherwise. Conditional on K=1 or 2,
3 answers
4,929 views
Determine whether each of the following statement is true (i.e., always true) or false (i.e., not always true).
1. Let X be a
3 answers
3,882 views
This figure below describes the joint PDF of the random variables X and Y. These random variables take values in [0,2] and
5 answers
8,124 views
For each one of the following figures, identify if it is a valid CDF. The value of the CDF at points of discontinuity is
4 answers
4,299 views
The joint PMF, pX,Y(x,y), of the random variables X and Y is given by the following table:
(see: the science of uncertainty) 1.
3 answers
7,292 views
Answers (83)
x_1 minXi i c=0.29957
true value for c = 0.29957
The true value for c = 0.29957
1 7/9 0.40343
p(XY >= 1) = 0.40343
please solve P(XY≥1)= 0.40343
3. 1.6 6.0.283333
answers to "Problem 1: Steady-state convergence" . Belonging to this very same problem set.... 1.a. False 1.b. False 2.a. False 2.b. False 3.a. True 3.b. True
answers to "Problem 1: Steady-state convergence" , belonging to this very same problem set.... 1.a. False 1.b. False 2.a. False 2.b. False 3.a. True 3.b. True
1. LW/(LW+LE) 2. LE*exp(-LE*x) 3. exp(-2*LW*t) 4. LE^7*v^6*exp(-LE*v)/720 5. 2*LW*LE/((LW+LE)^2) 6.a k-1 5.b LE^7*LW^(k-7)/(LE+LW)^k
1. lambda 2. Yes, it is a Poisson process. 3. lambda+mu 4. 1/mu 5. 2*20^n/(22^(n+1))
5. 2*20^n/(22^(n+1))
1. lambda 2. Yes, it is a Poisson process. 3. lambda+mu 4. 1/mu 5. 2*20^n/(22^(n+1))
the right answers are: 1)1/8 2)1/8 3)1/8 4)1/6 5)5/16 6)10/3
a=(lambda*s)^(m-n)*e^(-lambda*s) b= m-n c= lambda^m*s^(m-n)*t^n*e^(-lambda*(s+t)) d= m-n f= (s^(m-n)*t^n)/((s+t)^m) g= m h= m-n E[NM]= (lambda*t)*(lambda*s)+lambda*t+(lambda*t)^2
b) 41/17
17/10 41/17 b/a
1) 2*lambda*exp(-2*lambda*t) 2) lambda*e^(-lambda*x) 3) yes 4. 2*lambda*exp(-lambda*t)*(1-exp(-lambda*t)) 5) 3/(2*lambda)
1.1. h 1.2. 2.25/n 2. 22500 3. 90000 4. H-1.96*(3^0.5)/((4*n)^0.5), H+1.96*(3^0.5)/((4*n)^0.5)
1.1. h 1.2. 2.25/n 2. 22500 3. 90000
1.1. h 1.2. 2.25/n 2. 22500 3. 90000
5. H-1.96*(3^0.5)/((4*n)^0.5), H+1.96*(3^0.5)/((4*n)^0.5)
5. H-1.96*(3^0.5)/((4*n)^0.5), H+1.96*(3^0.5)/((4*n)^0.5)
4. Assume that X is uniformly distributed on [0,3]. Using the Central Limit Theorem, identify the most appropriate expression for a 95% confidence interval for h H-1.96*(3^0.5)/((4*n)^0.5), H+1.96*(3^0.5)/((4*n)^0.5)
The above answers are wrong, here is the official indictment: 1. 1/(theta*ln(2)) 3. x/(2*ln(2)) 4 . c1= 0.06452 c2= 0.58065
1. alpha = ln(mu/(2*lambda))/(mu-lambda)
the maximum number of tickets to be sold: 320
E[XY] = 3 var(X+Y)= 33 checked!!
2. P(X≤U)= 0.25
some answers P(X≥8)= 0.054799 var (X+Y) = 33 ?? (not really sure about this one) fellow classmate: help us out with E[XY] if you are reading this....Feel free to provide your answer to the whole TEST
1. mean = 40, variance = 24 2. mean = 50 3. mean = 50, variance = 24 4. mean = 0, variance = 0 the variance for question 2 is missing...Help us out, please!!
2.) 1/3*e^(-μ*α) + 2/3*(1-(e^-λ*α)) please, share what you have got for the whole problem set!!
1. p*2^(3-k) ------------------------ p*2^(3-k) + (1-p)*2^k 2. k ≤ 3/2 + 1/2*log_2(p/(1-p)) 4. it increases or stays the same please, if you are reading these answers ...Dont be selfish and share the other answers to the whole problem set
For 0≤q≤1, fQ∣A(q)= 4*q^3 P(B∣A) = 0.8 if you are reading these answers. Don't be selfish! you should share the other answers to the whole problem set....
2. Find the MAP estimate of Θ based on the observation X=x and assuming that 0≤x≤1. Express your answer in terms of x. For 0≤x≤1,θ^MAP(x)= x/2 PLEASE, if you are bugged with this problem set. Do not be mean and provide the other answers
Let N^=c1A+c2 be the LLMS estimator of N given A. Find c1 and c2 in terms of p. c1= 1-p PLEASE, could you help out by giving away the answer for c2 ???
3. second choice q = k/sum(k, i=1) t_i
c2 = n*ln(1) please! if you are reading this, be generous and provide your answers for the whole problem set
1.Carry out this minimization and choose the correct formula for the MAP estimate, θ^1, from the options below. (second choice) θ^1=∑ni=1ti(yi−θ0−θ2t2i)σ2+∑ni=1t2i 4. t1 and t2 = 10 IF YOU ARE READING THIS. PLEASE, PROVIDE YOUR ANSWERS TO THE
For general fX, when y>0, fY(y)= Solution: f_x(ln(y))/y When fX(x) = {1/3,0,if −2
1. Are X and Y independent? NO 2. Find fX(x). Express your answers in terms of x using standard notation . If 0
1. a= 0.4286 2. For 0≤y≤1, fY(y)= 0.6429 For 1
1 P(X>0.75)= 0.2266 2 P(X≤−1.25)= 0.1056 Let Z=(Y−3)/4. Find the mean and the variance of Z. 3. E[Z]= -0.25 4. var(Z)= 0.5625 5. P(−1≤Y≤2)= 0.3413
1 P(X>0.75)= 0.2266 2 P(X≤−1.25)= 0.1056 Let Z=(Y−3)/4. Find the mean and the variance of Z. 3. E[Z]= -0.25 4. var(Z)= 0.5625 5. P(−1≤Y≤2)= 0.3413
2. 0.01622
1. p*(1-p) 2. n*p*(1-p) 3. p*(1-p) 4. 0 5. p^2*(1-p)^2 6. 57/64
c= 5/64 P(Y
1. 1/n! 2.(n-m)!/n! 3. 1/(n m) 4. (1-p)^m 5. (n m)*(1-p)^m * p^(n-m)
4. c1=3, c2= 4, c3=6
1. (6 2)*(1/4)^2*(3/4)^4 3. 0.05 4. c1=3, c2= 4, c3=6
