Problem No-3 Implement the following two-level function using multi-level NOR gates: f(x1,X2.X3,X4,X5,X6,x7)=X1X«X5+X\X4X¢+> kaX4X6+X2X3X7 [9] Assume that logic gates have a maximum fan in of 2 and the input variables are available in uncomplemented form only (The number of gates required is shown in parenthesis).
X1, X2, X3, X4,X5,X6,X7,X8 are independent identically distributed random variables. Their common distribution is normal with mean 0 and variance 4. Let W = X12+ X22 + X32 + X42+X52+X62+X72+X82 . Calculate Pr(W > 2)
; Let at be a linear transformation as follows : T{x1,x2,x3,x4,x5} = {{x1-x3+2x2x5},{x2-x3+2x5},{x1+x2-2x3+x4+2x5},{2x2-2x3+x4+2x5}] a.) find the standard matrix representation A of T b.) find the basis of Col(A) c.) find a basis of Null(A) d.) is T 1-1? Is T onto?
Question 6: [12 Marks: 5, 3, 41 Let X1, X2, ..., X6 be a random sample from a population following a Gamma distribution with parameters a and B. Consider the following two estimators of the mean (a/b) of this distribution. Ô2 = X And ôz = ž (X1 + X2 + X3) +ś (X4 + X5 + X3) Where I = (X1 + X2 + ... + X6) (a) Determine the sampling distribution of 7 using moment generating functions. (b)...
Consider the following linear transformation T: R5 → R3 where T(X1, X2, X3, X4, X5) = (*1-X3+X4, 2X1+X2-X3+2x4, -2X1+3X3-3x4+x5) (a) Determine the standard matrix representation A of T(x). (b) Find a basis for the kernel of T(x). (c) Find a basis for the range of T(x). (d) Is T(x) one-to-one? Is T(x) onto? Explain. (e) Is T(x) invertible? Explain
2. Let Xi, X2, X3, X4,X5 be a random sample of size 5 from a popula- tion following the standard normal distribution (mean 0 and variance 1), and let X Σ5 i Xi/5. Let 6 be another independent observation from the same popula- tion. What is the distribution of (b) Z-Σ51 (Xi-X)2, Why?
Question 19 Find the pivot in the tableau. X1 X2 X3 X4 X5 X6 Z 2 3 6 1 0 0 0 10 2 1 2 0 0 0 20 4 04 0 0 1 040 -2 4 -8 0 1 0 یہ نہ مانم plonu 1 oloor 1 in row 2, column 5 6 in row 1, column 3 O 3 in row 1, column 2 4 in row 3, column 1 Question 16 5 p Write the expression...
If x1 ,x2 ,x3 ,x4 ,x5 be a sample from b(1,p) where p is unknown and 0<=p<=1 test Ho:p = .5 vs H1:p ≠ .5
For the data x1 = -1, x2 = -3, x3 = -2, x4 = 1, x5 = 0, find ∑ (xi2).
3. Description of each X and data for 27 franchise stores are given below The data (X1, X2, X3, X4, X5, X6) are for each franchise store. X1 annual net sales/$1000 X2 number sq. ft/1000 X3 - inventory I$1000 X4- amount spent on advertising /$1000 X5 size of sales district/1000 families X6 number of competing stores in distric X1 X2 X3 X4 X5 X6 231 3 294 8.2 8.2 11 156 2.2 232 6.9 4.1 12 10 0.5 149 3...