📘 probability and statistics

1. Given the survey data: | Mode | Male | Female | Total |

1. **Problem statement:** We are given two numbers whose arithmetic mean (AM) is 13 and geometric mean (GM) is 12. We need to find the two numbers and their harmonic mean (HM). 2.

1. **Problem statement:** We have three parts involving different probability distributions: binomial, Poisson, and normal.

1. The first question asks: "A variable that can take on a countable, finite value." This describes a discrete random variable. 2. The formula for discrete random variables is that

1. **Problem B: Classify the random variables as discrete or continuous.** 2. **Discrete random variables** take countable values, often integers.

1. **Problem:** Find the selling price for Trial 1 using the random number 81. - Selling Price probabilities:

1. **Problem Statement:** We will learn about the Normal Distribution, a key concept in probability and statistics used to calculate probabilities for continuous random variables.

1. **Problem 1: True or False statements about probability and distributions** (a) Given $B \subset A$ and $P(B) > 0$, check if $P(A|B) \leq P(B|A)$.

1. Problem Q.1 (a): Given $P(A)=0.3$, $P(B)=0.4$, and $P(A \cap B)=0.2$, find $P(A|B)$ and $P(A|B^c)$. Formula: Conditional probability $P(A|B) = \frac{P(A \cap B)}{P(B)}$. Also, $

1. **Problem 1: Find marginal distributions and conditional distribution** Given joint pmf: $$P(x,y) = K(2x + 3y)$$ for $$x=0,1,2$$ and $$y=1,2,3$$.

1. **Problem a**: Develop a formula for a random variate generator for the random variable $X$ with p.d.f. $$f(x) = \begin{cases} e^{2x} & -\infty < x \leq 0 \\ e^{-2x} & 0 < x < \

1. **Problem statement:** (a) Transform random numbers uniform on $[0,1]$ to uniform on $[-11,17]$.

1. **Problem Statement:** We have three random variables \(X, Y, Z\) with normal distributions: - \(X \sim N(100, 100)\), meaning mean \(\mu_X = 100\) and variance \(\sigma_X^2 = 1

1. The problem appears to involve probability and statistics concepts in the context of a category or assessment. 2. Since no specific question or data is provided, I will explain