Your exercise routine requires you to travel to the gym, complete your workout, and return home. Suppose that the proportion of the total time for travel to the time at the gym follows a beta distribution with α = 0.5 and β =1.   What is the probability that the proportion of time for travel to the gym exceeds 0.68?

How would you combine two vectors `a` and `b` as columns in R?

The random variable X has probability distribution. x 1 3 5 7 9 P(X=x) 0.2 p 0.2 q 0.15   Given that E(X) = 4.5, find the values of p and q.

The number of flaws in bolts of cloth in textile manufacturing is assumed to be Poisson distributed with a mean of 0.1 flaw per square meter. What is the probability that there are two flaws in 10 square meters of cloth?

How does the concept of relative frequencies enhance the interpretability of frequency distributions?

What distinguishes a cumulative relative frequency distribution from a cumulative frequency distribution?

We model the gene mutation of a virus as a Poisson process. Suppose a virus mutates once every 3 months on average.  What is mean time until the fifth mutation?

For a variable measured to the nearest tenth of a unit, what is a crucial consideration when establishing interval boundaries?

A 40 week male weighs 4.2 kg and his IV fluids are at 12 ml/hr. His potassium comes back at 3.1 and his sodium 129. A. What are the total fluids? B. How much potassium would you add to a 500 ml bag to give 3 mEq/kg/day potassium? C. How much sodium would you add to a 500 ml bag to give 4 mEq/kg/day sodium?

A 3.475 kg infant had 13 ml urine out over the last 8 hr. He has D10W infusing via PIV at 9 ml/hr. A. What is his urine output? B. In response to his urine output, you want to increase his TF to 90 ml/kg/day. What is his new IV rate?