WO07 20PJONY 0.75 The error function is defined by 0.50 0.25 1. %3D sTo- for all values of c. 001- There is no antiderivative of e-t which is an elementary function, ie. one which can be formed from polynomial, root, exponential, logarithmic, trigonometric functions. Yet the error function has significant uses in probability, statistics, and other fields; so computing accurate estimates is important. (a) Use a Riemann sum with 4 subintervals to estimate the value erf(0.2). (b) By replacing e-t² integrated), find another estimate for the value of erf(0.2). with its degree four Taylor polynomial about a = 0 (which can be (c) Repeat parts (a) and (b) for the value erf(2) (d) Provide sketches for parts (a)-(c). For example, sketch Riemann sums and regions beneath appropriate curves. (e) Are accurate estimates obtained in parts (a)-(c)? Why or why not? What changes would result in more accurate estimates? 2. For a givem constant B, consider the series e B(k+1). 0=Y (a) For what values of B is it possible to compute -23 -38 +...? %23 1 of 1 Automatic Zoom with its degree four Taylor polynomial about a = 0 (which can be (b) By replacing integrated), find another estimate for the value of erf(0.2). (c) Repeat parts (a) and (b) for the value erf(2) (d) Provide sketches for parts (a)-(c). For example, sketch Riemann sums and regions beneath appropriate curves. (e) Are accurate estimates obtained in parts (a)-(c)? Why or why not? What changes would result in more accurate estimates? 00 2. For a given constant 3, consider the series e-B(k+1). 0=Y (a) For what values of 3 is it possible to compute 00 =De-B(k+1) g- -23 -33 +...? 0=Y (b) For what values of B does a diverge? 0=C (c) For what values of B does > a converge? To what value does a converge in such 0=C 0=C cases? Ay
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.
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