A binomial random variable has an expected value, E(X) = 4 based on n=11 trials. What is the probability (p) of a success? Show all work/calculations for full credit.

lecture 7-10 PS 6-9 binomial formula mc, Take Home PCX= K ) = C" P" CI-P)" D -k formulas Classical approach oh = number of trials . pea) = number of outcomes favorable to A Total number of possible outcomes OK = # of successes Crandom variables empirical Cexpenments) O P= probability of a . PCa) =# of times event DID occur dunn Success a large # or expenments Total # of experiments Conducted expected value of binomial Probability Collecting data | observation o expected value = n x p Special Rule of addthon . Pca or b) = PCa) + PCb) o events = mutually exclusive ( disjoint) variance of binomal probability disjoint= when one event occurs, no other events can occur @"same time ovariance = np ( 1 - P) general rule of addition Standard deviation of binomal probability PCAor b) = P ca) + pcb) - Pca and b) Joint probability sd = nxpc i - D o events * mutually exclusive . not disjoint = When one event occurs. another can occur at same time normal random continuous variable general rule of mulhplicahon) opca and b) = pcal x pcb/a) n = CM, 5) conditional probabilil n( 3500, 500) o not Independent of each other . 50 Special Rule of multipiccation o pca and b) = P(a) x PCb) hean = median = mode X event a and b = Independent area = Probability combination Rule - counting rule C : n = distinct items " R ! CD - R J ! convert normal distribution and probabiting question Size of sequence = factonals to standard normal distribution Compliment Rule o PC-a) = 1-pca) I use the standard normal tables from lecture 3 To get area under . compliment rule = probability that an event does not occur Standard normal distribution . expected value (mean) of discrete random variable (table a ) . ECX) = E {x . PCx)} variance of discrete discrete random vanables var cx) = [(X-ecx))"?x P CX) ] ecx ) = expected Value I take each x value and Subtract by expected value 2) raise each part to and power 3 multiply each step 2 by associated probability I som up the column In step 3 = var cx ) Standard deviation of discrete random vanable O ( x ) = sq. root of var (x )