Assignment 1 - IIT Kharagpur
... 35. Suppose that radioactive particles strike a target according to Poisson process at an average rate of 3 particles per minute. What is the probability that 10 or more particles will strike the target in particular 2-minute period? 36. A telephone exchange receives calls at an average rate of 16 ...
... 35. Suppose that radioactive particles strike a target according to Poisson process at an average rate of 3 particles per minute. What is the probability that 10 or more particles will strike the target in particular 2-minute period? 36. A telephone exchange receives calls at an average rate of 16 ...
Chapter 4 - University of South Alabama
... Rule: If an experiment consists of two steps and first step consists of n1 outcomes and second step consists of n2 outcomes then there are n1*n2 final outcomes Example: tossing two coins consists of two steps. First step first coin two outcomes Second step- second coin two outcomes. Then |S| = # mem ...
... Rule: If an experiment consists of two steps and first step consists of n1 outcomes and second step consists of n2 outcomes then there are n1*n2 final outcomes Example: tossing two coins consists of two steps. First step first coin two outcomes Second step- second coin two outcomes. Then |S| = # mem ...
STP 421 - Problem Set 2 Solutions (Fall 2016) 1.) A jar contains 50
... 2.) Suppose that an HIV-1 test has a false positive rate of 0.1% and a false negative rate of 0.1%. If an individual with no known risk factors from a population with an HIV-1 prevalence of 0.001 is tested twice and receives a positive result both times, what is the probability that they are actuall ...
... 2.) Suppose that an HIV-1 test has a false positive rate of 0.1% and a false negative rate of 0.1%. If an individual with no known risk factors from a population with an HIV-1 prevalence of 0.001 is tested twice and receives a positive result both times, what is the probability that they are actuall ...
Discrete Random Vars.
... Definition. A random variable is a real-valued function X defined on a sample space Ω . This function X is called a discrete random variable if it has a countable range (either finite or denumerable.) Example 1. Roll two dice. Let X be the sum. Here Ω = {( ω1 , ω 2 ) : ω i ∈{1, 2, . . ., 6}} . Then ...
... Definition. A random variable is a real-valued function X defined on a sample space Ω . This function X is called a discrete random variable if it has a countable range (either finite or denumerable.) Example 1. Roll two dice. Let X be the sum. Here Ω = {( ω1 , ω 2 ) : ω i ∈{1, 2, . . ., 6}} . Then ...
2Prob Distn
... PROBABILITY DISTRIBUTIONS Expected values of discrete random variables Example: Examine the probability distribution for x ( the number of heads observed in the tossing of two fair coins) In a large number of experiments, 1/4 should result in x=0, 1/2 in x=1 and 1/4 in x=2 ...
... PROBABILITY DISTRIBUTIONS Expected values of discrete random variables Example: Examine the probability distribution for x ( the number of heads observed in the tossing of two fair coins) In a large number of experiments, 1/4 should result in x=0, 1/2 in x=1 and 1/4 in x=2 ...
Probability and Random Variables
... Sample space: Set of all possible outcomes of an experiment, S. For example, consider the experiment of two coins flipped at once: S = {(h, h), (h, t), (t, h), (t, t)} Or consider the experiment of a dart thrown at a (very large) target: S = R2 = {x, y : −∞ < x < ∞, −∞ < y < ∞} An event E is a subse ...
... Sample space: Set of all possible outcomes of an experiment, S. For example, consider the experiment of two coins flipped at once: S = {(h, h), (h, t), (t, h), (t, t)} Or consider the experiment of a dart thrown at a (very large) target: S = R2 = {x, y : −∞ < x < ∞, −∞ < y < ∞} An event E is a subse ...
Hydrologic Statistics
... • Random sampling: the likelihood of selection of each member of the population is equal – Pick any streamflow value from a population • Stratified sampling: Population is divided into groups, and then a random sampling is used – Pick a streamflow value from annual maximum series. • Uniform sampling ...
... • Random sampling: the likelihood of selection of each member of the population is equal – Pick any streamflow value from a population • Stratified sampling: Population is divided into groups, and then a random sampling is used – Pick a streamflow value from annual maximum series. • Uniform sampling ...
Basic Probability
... Probability – the chance that an uncertain event will occur (always between 0 and 1) Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1) ...
... Probability – the chance that an uncertain event will occur (always between 0 and 1) Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1) ...
Document
... S HHH , HHT , HTH , THH , TTH , THT , HTT , TTT assume that the outcomes of S3 are equiprobable, then the probability of each of the eight elementary events is 1/8. This probability assignment implies that the probability of obtaining two heads in three tosses is, by Corollary 3, ...
... S HHH , HHT , HTH , THH , TTH , THT , HTT , TTT assume that the outcomes of S3 are equiprobable, then the probability of each of the eight elementary events is 1/8. This probability assignment implies that the probability of obtaining two heads in three tosses is, by Corollary 3, ...
34 Probability and Counting Techniques
... All the examples discussed thus far have been experiments consisting of one action such as tossing three coins or rolling two dice. We now want to consider experiments that consist of doing two or more actions in succession. For example, consider the experiment of drawing two balls in succession and ...
... All the examples discussed thus far have been experiments consisting of one action such as tossing three coins or rolling two dice. We now want to consider experiments that consist of doing two or more actions in succession. For example, consider the experiment of drawing two balls in succession and ...
File
... b. P(none are greater than or equal to 3) c. P(at least one number is a multiple of 3) d. P(the first 5 you get is on the third roll) 5. According to the Masterfoods company, the distribution of colors for M&M Mini’s is: 25% blue, 25% orange, 12% green, 13% yellow, 12% red, and the rest are brown. a ...
... b. P(none are greater than or equal to 3) c. P(at least one number is a multiple of 3) d. P(the first 5 you get is on the third roll) 5. According to the Masterfoods company, the distribution of colors for M&M Mini’s is: 25% blue, 25% orange, 12% green, 13% yellow, 12% red, and the rest are brown. a ...
Chapter 7
... Continuous Random Variables • A continuous random variable X takes on all values in an interval of numbers. • The probability distribution of X is described by a density curve. The probability of any event is the area under the density curve and above the values of X that make up that event. ...
... Continuous Random Variables • A continuous random variable X takes on all values in an interval of numbers. • The probability distribution of X is described by a density curve. The probability of any event is the area under the density curve and above the values of X that make up that event. ...
