Modelling 2 Week 3: Discrete Random Variables Stephen Bush Department of Mathematical Sciences MM2: Statistics - Week 3 - 1 Random Variables • Reference: Devore § 3.1 – 3.5 • Definitions: • An experiment is any process of obtaining one outcome where the outcome is uncertain. • A random variable is a numerical variable whose value can change from one replicate of the experiment to another. • Sample means and sample standard deviations are random variables • They are different from sample
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Assignment Q1Find the parameters of binomial distribution when mean=4 and variance=3. Q2. The output of a production process is 10% defective. What is the probability of selecting exactly two defectives in a sample of 5? Q3. It is observed that 80% of television viewers watch “Boogie-Woogie” Programme. What is the probability that at least 80% of the viewers in a random sample of five watch this Programme? Q4. The normal rate of infection of a certain disease in animals is known to
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5.1 #12 ‚ #34a. and b‚ #40‚ 48 #12. Which of the following numbers could be the probability of an event? 1.5‚ 0‚ = ‚0 #34 More Genetics In Problem 33‚ we learned that for some diseases‚ such as sickle-cell anemia‚ an individual will get the disease only if he or she receives both recessive alleles. This is not always the case. For example‚ Huntington’s disease only requires one dominant gene for an individual to contract the disease. Suppose that a husband and wife‚ who both have a dominant
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variable The variable is the important aspects of the research. In research the concept are measure from variable. Variable are anythings that can take on differing or varing values. it mean that the value of variable vary from person to person‚ time to time or place to place but the meaning of variable are same to all. Thus variable are the charactestics of person‚ groups‚ objects‚ ideas‚ feeling or other thing that researcher want to measure. Variables are thus anything that can take on differing
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of five babies are randomly selected. In each group‚ the random variable x is the number of babies with green eyes (based on data from a study by Dr. Sorita Soni at Indiana University). (The symbol 0+ denotes a positive probability value that is very small). X | P(x) | 0 | .528 | 1 | .360 | 2 | .098 | 3 | .013 | 4 | .001 | 5 | 0+ | P(x) = .528 + .360 + .098 + .013 + .001 + (0+) = 1 This is a probability distribution because P(x) = 1 for the data given Standard Deviation = 4.9344
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Introduction The word Probability derives from probity‚ a measure of the authority of a witness in a legal case in Europe‚ and often correlated with the witness ’s nobility. In a sense‚ this differs much from the modern meaning of probability‚ which‚ in contrast‚ is used as a measure of the weight of empirical evidence‚ and is arrived at from inductive reasoning and statistical inference. A short history of Probability Theory............ The branch of mathematics known as probability theory was inspired
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Advantages and disadvantages of variable costing Many managers use variable costing for internal reporting and decision making since it has number of advantages (Myers par. 1). First‚ on variable costing reports costs are organized by behavior which makes it easier to understand. Also‚ variable costing statements facilitate cost volume profit (CVP) analysis because it separates cost behavior by fixed and variable. Under variable costing‚ changes in inventory or production do not affect the
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Basic Probability Notes Probability— the relative frequency or likelihood that a specific event will occur. If the event is A‚ then the probability that A will occur is denoted P(A). Example: Flip a coin. What is the probability of heads? This is denoted P(heads). Properties of Probability 1. The probability of an event E always lies in the range of 0 to 1; i.e.‚ 0 ≤ P( E ) ≤ 1. Impossible event—an event that absolutely cannot occur; probability is zero. Example: Suppose you roll a normal die
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Poisson distribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business‚ number of customers in waiting lines‚ number of defects in a given surface area‚ airplane arrivals‚ or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies‚ e.g.‚ to model the number of prairie dogs found in a square mile of prairie. The major difference between Poisson and Binomial distributions
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consumption rates. These approaches may be limited in effectiveness because of the relatively low variable cost of medical care. Variable costs (for medication and supplies) are saved if a facility does not provide a service while fixed costs (for salaried labor‚ buildings‚ and equipment) are not saved over the short term when a health care facility reduces service. OBJECTIVE: To determine the relative variable and fixed costs of inpatient and outpatient care for a large urban public teaching hospital
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