1 (Interview) A company is interviewing candidates for a data-scientist position. Theyestimate that the probability of a candidate being well qualified is 0.25. This is modeledby a random variable ğ that equals 1 with probability 0.25, and -1 with probability0.75. Candidates are interviewed separately by two interviewers. The decision of theinterviewers are modeled as two random variables i1 = ērg and i, = ēzğ, where ē, and é,are random variables that model the probability that the interviewers make a mistake.They both equal 1 with probability 0.8 (no mistake) and -1 with probability 0.2 (mistake).ē1, ē2, and q are all mutually independent.(a) What is the probability that the outcome of both interviews is positive, i.e. that= 1 and i, = 1?(b) Are i and iz independent?(c) Are i and iz conditionally independent given q?

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(Interview) A company is interviewing candidates for a data-scientist position. They estimate that the probability of a candidate being well qualified is 0.25. This is modeled by a random variable q that equals 1 with probability 0.25, and -1 with probability 0.75. Candidates are interviewed separately by two interviewers. The decision of the interviewers are modeled as two random variables = ēig and i2 = ēzğ, where e and é2 are random variables that model the probability that the interviewers make a mistake. They both equal 1 with probability 0.8 (no mistake) and -1 with probability 0.2 (mistake). ē1, ē2, and q are all mutually independent. (a) What is the probability that the outcome of both interviews is positive, i.e. that 1 = 1 and i, = 1? (b) Are i and i2 independent? (c) Are i1 and i, conditionally independent given q?