0 Consider continuous r. V. X w the following p. def.: $(x) = for os x...
following p. def.: Consider continuous r... X w/ the -X $(x) = otherwise Ta Find E(X). 4 81 for osx=3 a 15 Find Pla=X=4).
V.+w Operation in the triode reglon Condition v. e Wov 20 Vos uov os os-V (2) p V, so onl+Pala Characteristics Same relationships as for NMOS trasistos tCharacteristics: a CuGs- V,) ®os- } ip.C Replace .and NA with p,,and Nprespectively. V.V V, and yare negative. 2 wov ps For vos 2( -V) e Conditions for operation in the triode region ip lvi Q1. (10 points) For the following configuration of the given figure below, with the following parameters: VDD= +10...
-l 2. Consider the continuous-time signal: 0 x(t)- 1sts1 0, otherwise Find the Fourier transform X(a) of x(t). Simplify ths expression as much as po e simplest expression does not involve any complex numbers.) Draw a rough plot of o) as a function of w. Identify the peak value of X(w). Identify the location of the X( first null on either side of the vertical axis.
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
1. Find Fx in terms of φ (t). Is X a continuous random variable ? 2. Compute p(X 0) 3. Compute E(X). Hint: use the CDF expectation formula, and integration by parts. You may assume that lim, t"o(-t) 0 for all n 2 0. 4. Find the CDF Fx (u) 5. Compute V(X). Hint: use Fxa, and follow the same hint of part (3) 1. Find Fx in terms of φ (t). Is X a continuous random variable ? 2....
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
1 0 < x < 1, 2. Consider the Haar scaling function, p(x):= { +, and (x) := { -1 10 otherwise 0 0 < x < 1/2, 1/2 < x < 1,. Sketch (by hand is okay) 7(2x) and 7(2x – 1). Show these functions form an orthogonal set. Find the otherwise corresponding orthonormal set. in 3. Let V be a vector space with a complex inner product (,) > Suppose that the set S= {U1, U2, ..., Un}...
X with density fcx)3/56 ir 2<<4 5. Consider a continuous random variable X with density f(x)- otherwise a. Find P(1 <X<3) b. Find ECX)
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider • the parallelogram B = {s(3v) + t-w) 0 <s,t<1, s,te R} spanned/formed by the vectors (3v) and (-w), and • the parallelepiped P = {ru + s(3v) + (-w) 0 <T,,t<1, r, s, t€ R} [10] spanned formed by vectors u. (3v). and (-w) We take the parallelogram B as a base of P. (a) Does the ordered vector triple (v xw, 3v, -w),...
Problem(2) (5 points) A continuous distribution has density function k sin(r); 0rST 0; f(x) = otherwise. (a) Find the numerical value of k so that f(r) is a density function. (b) Find E[X] (c) Find E[X2. (d) Find Var X] Problem(2) (5 points) A continuous distribution has density function k sin(r); 0rST 0; f(x) = otherwise. (a) Find the numerical value of k so that f(r) is a density function. (b) Find E[X] (c) Find E[X2. (d) Find Var X]