1. Summation notation. Simplify each summation and state what property of summation you've used to make the simplif...
1. Summation notation. Simplify each summation and state what property of summation you've used to make the simplification. Note: X and Y are random variables and k is a constant. (b) ¿xx (c) (x + ya WEDI
Convert the following summations to summation notation, then use Table 5.1 in the book to simplify and find the sum. a.) 2 +5+8+ + 22. b.) 4+4+4+ ... +4, where there are 103 terms. c.) 1+4+9+ 25 + ... + 100. What is the pattern here?
Simplify the following indicial expressions as much as possible. ΣΣ1C,B (a) Substitute Cii = -1 AipBpj into a = k 1 Hint: Consider changing the index j to index k in the expression for C;i 3 ( b) Σ-Σ_ Σ1 Α, Βιδικ - Σ Σ Σ-12AB , im rį=1 i=1 m=1 Hint: Use the index substitution property of Kronecker delta first to simplify the expression. When you do that, the triple summation will reduce to double summation in each symbol...
State the number in scientific notation and write the number of significant figures in each of the following numbers. Explain your answer. 1. a. 37.60 b. 0.0130 c. 13000 d. 1.2300 Perform the indicated operations to the correct number of significant figures using the rules for significant figures 2. a. 37.60 x 1.23 b. 6.7/8.975- c. 3.765+1.2+37.21 To get credit, specify the rule you used to round your results 3. Three students make measurements (in m) of the length of...
he second form for one-parameter exponential family distributions, introduced during lecture 09.1, was Jy (y | θ) = b(y)ec(0)t(y)-d(0) Let η = c(0). If c is an invertible function, we can rewrite (1) as where η is called the natural, or canonical, parameter and K(n) = d(C-1(n)). Expression (2) is referred to as the canonical representation of the exponential family distribution (a) Function κ(η) is called the log-normalizer: it ensures that the distribution fy(y n) integrates to one. Show that,...
Suppose X has a Poisson(λ) distribution (a) Show that E(X(X-1)(X-2) . .. (X-k + 1)} for k > 1. b) Using the previous part, find EX (c) Determine the expected value of the random variable Y 1/(1 + X). (d) Determine the probability that X is even. Note: Simplify the answers. The final results should be expressed in terms of λ and elementary operations (+- x ), with the only elementary function used being the exponential
2. Explain in words, and words only, the following properties of expected values. NOTE: X and Y are random variables and k is a constant. (a) E(k) = k (b) E(X+Y) = E(X) + E(Y) (c) E(X/Y) + E(X)/E(Y) (d) E(X+Y) E(X)*E(Y) (unless what?) (e) E(X2) # (E(X)]? (1) E(kX) = E(X) 3. For random variable X with mean H. variance is defined var(X) = Ef(X-M.)'. Show how variance can be expressed only in terms of E(X) and E(X). 4....
2. Explain in words, and words only, the following properties of expected values. NOTE: X and Y are random variables and k is a constant. (a) E(k) = k (b) E(X+Y) = E(X) + E(Y) (c) E(X/Y) + E(X)/E(Y) (d) E(X+Y) E(X)*E(Y) (unless what?) (e) E(X2) # (E(X)]? (1) E(kX) = E(X) 3. For random variable X with mean H. variance is defined var(X) = Ef(X-M.)'. Show how variance can be expressed only in terms of E(X) and E(X). 4....
MA-119 Review for Final Exam: Fall 2019 Simplify completely and express in terms of positive exponents 2. Find the slope interest form of the equation of the line that is perpendicular toy passes through the point. 51 ) 3. Find the slope-intercept form of the equation of the line through the points (-2) and (2 4. Solve for x and check the solution 3x+2 -1 -6 5. Factor completely: a) 12 -10-1815 b)x+ 5x-16x - 30 Based on the graph...
Derive ground state term symbols for each of the following atoms. Use notation 2S(1/2) for state 2S1/2 a) S b) Ca c) Si d) Cr