Basic Statistics And Probability By Shahid Jamal Pdf 745 Exclusive Now

Why dispersion? Two datasets can have same mean but different spread.

Key Formulas:

Shortcut method (Assumed mean method) – extensively used in Shahid Jamal’s book.

Problem 745 Exclusive (Typical):
Calculate variance and standard deviation for: 5, 7, 9, 11, 13.
Solution: Mean = 9. Deviations: -4, -2, 0, 2, 4. Squares sum = 16+4+0+4+16=40. Variance = 40/5=8. SD = √8 = 2.828. Why dispersion

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Shahid Jamal is widely respected in the competitive exam circuit for his ability to simplify complex mathematical concepts.

Classical Definition: P(E) = Number of favorable outcomes / Total possible outcomes (equally likely).

Axioms (Kolmogorov):

Important Rules:

Independence: P(A ∩ B) = P(A) × P(B)

Exclusive Problem 745 (Bayes’ Theorem type):
Bag A has 3 red, 5 green. Bag B has 4 red, 2 green. One bag is chosen at random, and one ball is drawn. It is red. Find the probability it came from Bag A. Shortcut method (Assumed mean method) – extensively used

Solution using Bayes:
P(A|Red) = [P(A)×P(Red|A)] / [P(A)P(Red|A) + P(B)P(Red|B)]
= [0.5 × 3/8] / [0.5×3/8 + 0.5×4/6] = (3/16) / (3/16 + 4/12) = (3/16)/(9/48+16/48) = (3/16)/(25/48) = (3/16)×(48/25) = 9/25 = 0.36.

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| Measure | Formula (Raw Data) | Best Used For | |---------|--------------------|----------------| | Mean (x̄) | Σx / n | Symmetric data, no outliers | | Median | Middle value | Skewed data | | Mode | Most frequent | Categorical data |

Weighted Mean: x̄_w = Σ(wx) / Σw

Exclusive Problem (745 Style):
The mean of 20 numbers is 15. If each number is multiplied by 3 and then 4 is added, find the new mean.

Solution: New mean = 3×15 + 4 = 49.

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