Applied Mathematics - Probability & Statistics

Explore the types of data for measures of dispersion: ungrouped raw data and grouped data, including discrete, continuous, and class interval formats.

Explore the formula for the mean across raw data, discrete data with frequencies, and class interval data, and apply the assumed mean method and shift method to simplify computations.

Explore standard deviation as a measure of dispersion, deriving its formulas for raw, discrete, and continuous data, and compute it from the mean and variance.

Explore standard deviation for discrete data and class intervals, using the basic and assumed mean methods, and the shift of origin approach with frequency data.

Learn how deciles and percentiles partition data into ten parts and compute specific percentiles in continuous class intervals using lower limits, cumulative frequency, and percentile formulas.

Explore quartiles q1 and q3, compute quartile deviation as (q3 - q1) / 2, and learn methods to find these values for raw, discrete, and grouped data.

Explore a solved example of standard deviation for grouped data, using class intervals, midpoints, and frequencies, and apply the shift method to compute the mean, variance, and the standard deviation.

Identify the median as the data's central value and learn to compute it for raw data, discrete data, and class intervals using order and cumulative frequency.

Compute the median from grouped data using cumulative frequencies and the median formula; the example yields about 71.66 in the 65–75 class.

Calculate the probability of drawing two yellow pencils without replacement from a box of 5 green and 7 yellow pencils, and determine the sample space and the probability 7/22.

Explore three independent hitters A, B, and C with hitting probabilities 3/4, 1/2, and 5/8, and determine exactly one, exactly two, none, or at least one hit.

Compute the probability that at least one of two balls drawn without replacement is black using a complement, yielding 10/21.

we apply basic probability to life-table questions, deriving odds against a husband and wife reaching ages, then using independence to compute the union and exactly-one alive in 25 years.

Compute the odds in favor of winning at least two of three independent chess games, given a per-game win probability of 3/5.

Apply independent-event probability to compute not solved and exactly one solver, using p(x solves)=2/3 and p(y solves)=1/4, yielding not solved 1/4 and exactly one 7/12.

Compute probabilities for two events using sample space, union, and complement. Apply formulas to find B(A ∩ B), B(A ∪ B), and B(A complement) from given values.

Compute the probability that the problem is solved by using odds against, complement events, and independent events from John, Rafi, and Adolphe, yielding 16/21.

Determine how many green balls yield a probability of drawing two green balls equal to 1/7, by solving g choose 2 over (9+g) choose 2.

Solve a probability numericals problem by applying the union formula, complements, and basic arithmetic to find p(b|a) and p(a ∩ b).

Explore probability with a two day dice scenario, computing six on the first day and on the second day as 6/36. Compute the intersection 1/36 and verify independence, since P(A)×P(B)=P(A∩B).

Solve a numerical probability problem with three mutually exclusive events A, B, and C where exactly one occurs; convert odds against to probabilities and compute P(C) and odds against C.

Explains level-2 probability numericals through solved examples on conditional probability, Bayes theorem, binomial models, and sampling without replacement, with step-by-step calculations.

the lecture explores solved probability numericals, covering events, independence, conditional probability, binomial variance, replacement draws, venn-diagram problems, and a cube-root-of-unity probability puzzle.