Recent content by Bertrandkis

Thanks, You are the man Dick.

Homework Statement Suppose a random variable X has probability density function(pdf) f(x) { 1/3 for 1 \leq x \leq 4 find the density function of Y= \sqrt{X} The Attempt at a Solution y=g(x)=\sqrt{x} so g^-1(y)=x=y^2 A= \{ x: 1 \leq x \leq 4 \} is monotonic onto B= \{y: 1 \leq...

I managed to get the answer to the second part.an I got the time as 20.79. But for the first part I the probability of 0.28 is the one for the phone to ring once as I said earlier. The probability of the phone ringing ONCE or TWICE is not given. Does this mean P(X<=2)?

I made a mistake here I ommited the multiplication by \lambda hence the result I am getting is Probability that phone rings once-> P(X=1)=0.3333* e^{-0.33333}=0.2386 which is still different from 0.28 given in the book. How do I get to this value?

Homework Statement Phone calls are received at Diane residence have a Poisson distribution with \lambda =2. a) If Diane takes a shower for 10 min, what is the probability that the phone rings Once or Twice. b) How long can she shower if the probability of receiving no calls be at most 0.5...

To be honest, I don't know how to find a vector perpendicular to both V1 and V2. I can find 2 equations of a lines perpendicular to each of the vectors (1)=> (x,y,z)=(-1,1,2)+t(-1,1,1) (2)=> (x,y,z)=(-1,1,2)+t(1,1,1) now where do I go from here.

Homework Statement Let x and y be to vectors Verify whether |xy|<=|x|+|y| for all x,y The Attempt at a Solution My first problem with this question is that it does not tell us whether the operation xy is the same as x.y (dot product) or a cross product.

Homework Statement Let L be a line in R3 passing through(-1,1,2) and is perpendicular to vectors V1 (-1,1,-1) and V2 (1,1,1). Find an equation for L in parametric form. Homework Equations The Attempt at a Solution using vector V2 (x,y,z)(1,1,1)=(1,1,1)(-1,1,2) A possible...

I think what we want to know is this: What is the relationship betwen L1, L2 and L0? Is L0 perpendicular to these 2 lines, or is L0 parallel to these two lines? Does L0 intersects L1 and L2 at all?

for the first question I came up with this: 0=(A-I)^2=A^2-2A+I. so if Ax=\lambda x, for some vector x \neq 0, then A^2x=\lambda^2x, and 0=(\lambda^2 - 2\lambda + 1)x=(\lambda - 1)^2x. thus \lambda = 1. This looks very right, doesn't it? For question 2, I figue that x^2=1 yields x=+-1...

Question 1 is formulated correctly. They want T(1);T(t);T(t^{2}). Some one has suggested that : T(1)=1/2( T(1+t) - T(t+t^{2}) + T(1+t^{2}) )) becaused T being a linear transformation when the RHS expression is developed it yields T(1). The problem is solved by replacing T(...) in the RHS...

Question 1 Let T: P2 -> M22 be a linear transformation such that T(1+t)=\left[\begin{array}{cc}1&0\\0&0\end{array} \right]; T(t+t^{2})=\left[\begin{array}{cc}0&1\\1&0\end{array} \right]; T(1+t^{2})=\left[\begin{array}{cc}0&1\\0&1\end{array} \right]; Then find T(1),T(t),T(t^{2})...

Dick 1)How do you know that (A-I)(A-I)x=0? Why not (A-I)(A-I)x={\lambda}x. If (A-I)(A-I)x=0 and x being the eigen vector, this suggests that {\lambda}=0. 2)I know that det(A^{T})=det(A) but how does that prove that det(A)=+-1) ?

Question 1 Let u, v1,v2 ... vn be vectors in R^{n}. Show that if u is orthogonal to v1,v2 ...vn then u is orthogonal to every vector in span{v1,v2...vn} My attempt if u is orthogonal to v1,v2 ...vn then (u.v1)+(u.v2)+...+(u.vn)=0 Let w be a vector in span{v1,v2...vn} therefore...

Question 1 Let A be an nxn matrix such that (A-I)^{2}=O where O is the zero matrix Prove that if {\lambda} is an eigen value of A then {\lambda}=1 My attempt If (A-I)^{2}=O then A=I (1) if {\lambda} is an eigen value of A then Ax={\lambda}x (2) replace (1) in (2) Ix={\lambda}x , but...