Show that if the uniform variable x has an Erlang density with n=2‚ then Fx(x) = (1-e-cx-cxe-cx) U(x) Q 4-8‚ The random variable x is N (10; 1)‚ Find f (x | (x-10)2 <4) Q 4-9‚ Find f(x) if F(x) = (1-e-ax) U(x-c). Q 4-10‚ If x is N (0‚ 2) find a) P{1≤ x ≤ 2} b) P{1≤ x ≤2 | x ≥ 1} Q4-14‚ A fair coin is tossed 900 times and the random variable x equals the total number of heads. a) Find fx(x)‚ 1: exactly‚ 2: approximately Gamma Distribution eq. b) Find P {435
Premium Random variable Probability theory
Homework 3 Probability 1. As part of a Pick Your Prize promotion‚ a store invited customers to choose which of three prizes they’d like to win. They also kept track of respondents’ gender. The following contingency table shows the results: | MP3 Player | Camera | Bike | Total | Men | 62 | 117 | 60 | 239 | Woman | 101 | 130 | 30 | 261 | Total | 163 | 247 | 90 | 500 | What is the probability that: a. a randomly selected customer would pick the camera? 247/500= 0.494=
Premium Marketing Customer Customer service
consecutive points falling on one side of the centerline When the process is in statistical control‚ find the false alarm probability (Type-I error) for each case. The corresponding probability measures are obtained from the Normal table as P(3 " Z) = 0.00135 P(2 " Z) = 0.02275 P(1 " Z) = 0.1587 Solution: ! i) Use the Binomial distribution to ! calculate the probability measures. ! 3! 3! P(Y ! 2 n = 3‚ p = 0.02275) = (0.02275)2 (1" 0.02275) + (0.02275)3 = 0.00153 2!1! 3!0! Type-1
Premium Normal distribution Control chart Probability theory
Probability 1.) AE-2 List the enduring understandings for a content-area unit to be implemented over a three- to five- week time period. Explain how the enduring understandings serve to contextualize (add context or way of thinking to) the content-area standards. Unit: Data and Probability Time: 3 weeks max Enduring Understanding: “Student Will Be Able To: - Know what probability is (chance‚ fairness‚ a way to observe our random world‚ the different representations) - Know what the
Free Probability theory Normal distribution
TEM1116 Probability and Statistics Tri1 2013/14 Chapter 1 Chapter 1: Discrete and Continuous Probability Distributions Section 1: Probability Contents: 1.1 1.2 1.3 1.4 1.5 Some basics of probability theory Axioms‚ Interpretations‚ and Properties of Probability Counting Techniques and Probability Conditional Probability Independence TEM1116 1 TEM1116 Probability and Statistics Tri1 2013/14 Chapter 1 1.1 Basics of Probability Theory Probability refers to the study
Premium Random variable Probability theory
BINOMIAL THEOREM : AKSHAY MISHRA XI A ‚ K V 2 ‚ GWALIOR In elementary algebra‚ the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem‚ it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc‚ where the coefficient of each term is a positive integer‚ and the sum of the exponents of x and y in each term is n. For example: The coefficients appearing in the binomial expansion are known as binomial coefficients.
Premium
The binomial theorem is a simplified way of finding the expansion of a binomial to a certain power. We can of course find the expanded form of any binomial to a certain power by writing it and doing each step‚ but this process can be very time consuming when you get into let’s say a binomial to the 10th power. Example: (x+y)^0=1 of course because anything to the power if 0 equal 1 (x+y)^1= x+y anything to a power of 1 is just itself. (x+y)^2= (x+y)(x+y) NOT x^2+y^2. So expand (x+y)(x+y)=x^2+xy+yx+y^2
Premium Polynomial
WHAT IS A RANDOM VARIABLE? A random variable assigns a number to each outcome of a random circumstance‚ or‚ equivalently‚ a random variable assigns a number to each unit in a population. It is easier to create rules for broad classes of situations and then identify how a specific example fits into a class than it is to create rules for each specific example. We can employ this strategy quite effectively for working with a wide variety of situations Involving probability and random outcomes. We
Premium Random variable Probability theory
*the significance of the binomial system *why common names of plants should not be used to correctly identify plants. The scientific system to classify and naming plants are controlled and coordinated by botanist throughout the world. The system of classification in plants is to classify them in groups with similar characteristics. Then continue to divide and sub-group until you have one type of plant in each group. The main level of division in plants are as follows: Plants are divided into
Premium Plant Species Cell
STA1101 Normal Distribution and Continuous random variables CONTINUOUS RANDOM VARIABLES A random variable whose values are not countable is called a _CONTINUOUS RANDOM VARIABLE._ THE NORMAL DISTRIBUTION The _NORMAL PROBABILITY DISTRIBUTION_ is given by a bell-shaped(symmetric) curve. THE STANDARD NORMAL DISTRIBUTION The normal distribution with and is called the _STANDARD NORMAL DISTRIBUTION._ Example 1: Find the area under the standard normal curve between z = 0 and z = 1.95 from z
Premium Normal distribution Standard deviation Probability theory