1. Evaluate each sum. (a) IN DO (b) (-1) 435+1 k = 1 k7k 71 5 (c) 3! 41 - + 51 + ... for 1 and 2: https://www. desmos. com/calculatorwh4pxvqvv 2. Evaluate the sum. (a) In (-3 ) n 7 =2 4n+1 (b) > nen n= 1 (c) n(n-1) 20-2 (d) En2xmed n=0 3. The following summations are related to the Poisson distribution. Evaluate each sum. (a) Given ack K! = exp(x), evaluate )1k K = C K=0 KI exp(-A) (This is the sum of the probabilities in the Poisson probability distribution.) (b) Evaluate k! - exp(-A) (This is the mean of the Poisson distribution.) (c) Evaluate k(k - 1)1k -exp(->) K=0 k! (d) Evaluate K! 1 exp(-A) (e) Evaluate K 2x k =0 k! K=0 k! exp(-A) (This is the variance of the Poisson distribu- tion.) https://www. desmos . com/calculator/ctrzqg315d 4. Let f(x) = c)(-1) 3n-1 n=1 (n - 1)! Find the constant C so that f defines a valid probability density function on the interval [0, 2]