Bernoulli & Binomial distribution

CFA Level I Quant
#1

What is bernoulli random variable? it is a binomial random variable for which the number of trials is 1? example? Can you differentiate this from binomial?

Q. probability that DJIA will increase on any given day is 0.67. => p(UP) = 0.67. Movements in DJIA are independentof previous movements. What is the expected value of number of UP days in a 5 day period? And 5*0.67 = 3.35

Can anyone explain?

#2

A Bernoulli trial is tossing a coin: two outcomes (success and failure) with constant probabilities.

A binomial distribution is the distribution of a given number of Bernoulli trials: what’s the probability of getting k heads in n tosses of the coin?

The expected number of successes in n Bernoulli trials is:

E(successes) = n × P(success)