Master Complete Statistics For Computer Science - II

Leverage the binomial distribution to model the number of successes in independent trials, derive its pmf, and explore the moment generating function.

Explore the additive property of the binomial distribution, showing when sums of independent binomial variables remain binomial and how probability of success conditions affect this.

Explore the binomial distribution with solved examples on rocket launches, calculating the probability of exactly five successful launches and fewer than five.

Explore the Poisson distribution, derive its PMF and moment generating function, and apply it to counting events from zero to infinity using lambda.

Explore the Poisson distribution, its mean and variance, and how it arises as the limit of the binomial distribution with lambda.

Explain the additive property of the Poisson distribution, showing that the sum of independent Poisson variables is Poisson with a parameter equal to the sum of their lambdas.

Investigate the geometric distribution, define the pmf and derive the moment generating function, focusing on the number of trials until the first success in independent experiments.

Explore the memoryless property of the discrete geometric distribution, showing P(X>t+s) = P(X>t) P(X>s) and the independence from prior events.

Apply the geometric distribution to model independent road test attempts with a per trial success probability of 0.8, and find the first pass within the first three trials.

Delve into the hypergeometric distribution, derive its mean and variance, and use the expectation of X to understand how the distribution behaves.

Explore the hypergeometric distribution through a solved example involving five taxis and ambassadors, calculating the probability of at least three ambassadors among the five chosen.

Solve uniform distribution example 7 by analyzing two independent variables x and y on the unit interval. Compute the probability that |x−y| exceeds 1/4 using the unit-square region.

Explore solved example 4 on the exponential distribution, modeling repair time as x and computing probabilities such as p(x > 2) and conditional p(x > 9).

Explore Erlang distribution through solved example 1, calculating the probability that a city’s daily power consumption exceeds its 12 million kilowatt-hour capacity.

Explore the erlang distribution: derive its pdf, identify the mode at (k-1)/lambda for k>1, and compute the mean k/lambda and variance k/lambda^2 through a solved example.

Examine the normal distribution's probability curve, its bell-shaped density function, and how standard deviation sets the inflection points at ±σ, shaping the curve's spread and symmetry.

Examine the normal distribution, focusing on the mean mu and dispersion sigma, and compute the expectation E[X] for X drawn from this distribution.

Explore the normal distribution with an unknown mean, and learn how probabilities like P(X<6) are interpreted in a solved example 3.

solve a normal distribution example to compute the probability that x lies between 30 and 35 with a mean near 33, and explore raising expected profit by 50 percent.

Examine the normal distribution with an example, deriving the mean and standard deviation, applying change of origin and scale, and computing the approximate normal density and z-scores for a distribution.