Discrete Random Variables: Videos & Practice Problems

During a health survey, people are arranged in groups of $5$ and asked if they exercise regularly. The random variable $x$ denotes the number of people in each group who say yes. The given probabilities for $x=0,1,2,3,4,5$ are $0.05,0.15,0.30,0.30,0.15,0.05$ respectively. Confirm if this is a probability distribution and find the mean and standard deviation.