a)
| Class Interval | Observed Frequency (O) | Probability (P) | Expected Frequency (E )=25*P | (O-E)^2/E | |
| 0 | 10 | 8 | 0.41198 | 10.299584 | 0.513427 |
| 10 | 20 | 8 | 0.24225 | 6.0563267 | 0.623788 |
| 20 | 30 | 2 | 0.14245 | 3.561221 | 0.684431 |
| 30 | 40 | 5 | 0.08376 | 2.0940573 | 4.032604 |
| 40 | 50 | 2 | 0.04925 | 1.2313406 | 0.479833 |
| 25 | 6.334083 | ||||
b)
| Class Interval | Observed Frequency (O) | Probability (P) | Expected Frequency (E )=25*P | (O-E)^2/E | |
| 0 | 5 | 3 | 0.23317756 | 5.8294389 | 1.373327 |
| 5 | 11 | 5 | 0.20921496 | 5.230374 | 0.010147 |
| 11 | 20 | 8 | 0.21184389 | 5.2960973 | 1.380467 |
| 20 | infinity | 9 | 0.34576359 | 8.6440898 | 0.014654 |
| 25 | 2.778595 | ||||

Question 1 (40 pts) 5.0909 1.3371 13.5739 13.5765 36.8361 30.5131 7.30876 19.9367 0.541946 7.4161613.0638 14.5477 0.782948...
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distribution function if x<0 F(x)ax2 0.1x if osxs 20 if x> 20 0 Find 1) the coefficient a; 2) P 10); 3) P(X<30). 2. The result of some measurement X is normally distributed with parameters 184 and 8. Compute the probability that variable X takes value from interval (170;180) at least once in 5 experiments 3. Two independent random variables X...
2. Let X be an exponentially distributed random variable with parameter 1 = 2. Determine P(X > 4). 3. Let X be a continuous random variable that only takes on values in the interval [0, 1]. The cumulative distribution function of X is given by: F(x) = 2x² – x4 for 0 sxsl. (1) (a) How do we know F(x) is a valid cumulative distribution function? (b) Use F(x) to compute P(i sX så)? (c) What is the probability density...
Rubber rabbitbrush plants display heritable variation in plant height and insect-induced gall formation. In a field study, researchers investigated the relationship between plant height and gall number for the rubber rabbitbrush plants in a natural population. The researchers used the data they collected to perform a chi-square test of independence. The null hypothesis for the chi-square test was that plant height and gall number are independent. The data for the chi-square test are presented in Table 1. Table 1. Data...
please show me the step by step process of getting the correct
answer. only do so when you are certain, otherwise, please ignore.
thanks in advance.
1 pts Question 4 In one of Mendel's dihybrid crosses of peas, he observed round yellow, round green, wrinkled yellow, and wrinkled green F2 plants. He used the Chi Square test to see if the number of plants he observed in each category matched the expected 9:3:3:1 ratio. The Chi Square value he calculated...
I can do the first part of the question 1a, could
someone show me step by step how to do do 1b?
) Y.Ya..., Y, form a random sample from a probability distribution with cumu- lative distribution function Fy (u) and probability density function fr(u). Let Write the cumulative distribution function for Ya) in terms of Fy(y) and hence show that the probability density function for Yy is fy(1)(y) = n(1-Fr (v))"-ify(y). [8 marks] (b) An engineering system consists of...
Suppose that X is exponentially distributed with parameter 1 and let Y = µ −1X, where µ > 0 is a positive constant. Find the cumulative distribution function and the density of Y and use this to conclude that Y is exponentially distributed with parameter µ.
5. Let f(t) be the probability density function, and F(t) be the corresponding cumulative f(t) distribution function. Define the hazard function h(t) Show that if X is an 1-F(t): exponential random variable with parameter 1 > 0, then its hazard function will be a constant h(t) = 1 for all t > 0. Think of how this relates to the memorylessness property of exponential random variables.
For a particular gene associated with a degenerative neurological disorder, you surveyed genotype frequencies in a population and found that 16 people had genotype AA, 97 had genotype Aa, 15 had genotype aa. a) Calculate the allele frequencies. b) Calculate the expected genotype frequencies under Hardy-Weinberg Equilibrium. Use the chi-square test to determine whether the observed number of people with different genotypes and expected number of people with different genotypes are significantly different (at an alpha level of 0.05). What...
5. For X follows Exp(6) (exponential distribution with parameter θ), a hypothesis test rejects the null hypothesis Ho : θ-1 when X k versus H1 : θ > 1. (a) Show that for any k greater than -log(0.05), the test has the probability of type I error less than 0.05 (b) Show that the power of the test at θ-10 is larger when k-1 than k-2. (c) Let k-_ log(0.05), calculate the power function in terms of θ when θ...
EOC 13.30 Homework Unanswered This question is based on the same scenario as EOC 13.28: Suppose that you are interested in whether anxiety level and problem-solving are related. You administer a standard measure of anxiety to 50 people and use the results to classify them as either "high" or"low' in anxiety. You also give each person the JUMBLE (a puzzle) from the daily paper and observe whether or not they solve it. Is anxiety level related to problem-solving ability? Your...