Professor Chris McCarthy Mat 501 Notes Handout 7 (3d Ed.) Quiz 1 HW. Answer sheet. Answers on this page in the spaces provided. Put your work on bottom (after question 4, on back, or staple work). No work - no credit. Do not put work in the margins, or in the space provided for answers. Print this page on a printer. Staple everything with a stapler! 1. A an object of mass m is hung from a beam by a spring (with spring constant k) and dashpot (with damping constant parallel, exactly like in your notes. See figure below. The equilibrium height of the object is taken to be r 0 and at time t 0 the object is initially located at 2 and has an initial velocity of 4. Very neatly write the answers in the space provided. DO and upwards is the positive direction. Do not worry about gravity, etc. Suppose that m = 1, c 2, k =5 NOT SHOW YOUR WORK HERE. There is not enough space! Put work on back or attach with staple. (a) The IVP is: dashpot spring k (b) IVP's solution is: mass m (c) At t- 0.5 the object will be located at r(0.5) (3 decimal places) 2. Solve the IVP y' =-Ty, y(0) =-4. Answer (no work needed, memorize answer): 3. Solve the IVP y' = xy, y (V2)-5e. Answer: 4. Solve the IVP. -5 Answer 15est, (2) 20e10
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question 1
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