Let θ be a bernoulli random variable that indicates which one of two hypotheses is true, and let p(θ=1)=p. under the hypothesis θ=0, the random variable x is uniformly distributed over the interval [0,1]. under the alternative hypothesis θ=1, the pdf of x is given byfx∣θ(x∣1)={2x,0, if 0≤x≤1, otherwise. consider the map rule for deciding between the two hypotheses, given that x=x. suppose for this part of the problem that p=3/5. the map rule can choose in favor of the hypothesis θ=1 if and only if x≥c1. find the value of c1.

1. why is a frequency distribution useful? it allows researchers to see the "shape" of the data. it tells researchers how often the mean occurs in a set of data. it can visually identify the mean. it ignores outliers. 2. the is defined by its mean and standard deviation alone. normal distribution frequency distribution median distribution marginal distribution 3. approximately % of the data in a given sample falls within three standard deviations of the mean if it is normally distributed. 95 68 34 99 4. a data set is said to be if the mean of the data is greater than the median of the data. normally distributed frequency distributed right-skewed left-skewed