A Study to Evaluate the Safety, Tolerability, Immunogenicity and Vaccine-like Viral Shedding of MEDI-534, Against Respiratory Syncytial Virus (RSV) and Parainfluenza Virus Type 3 (PIV3), in Healthy 6 to <24 Month-old Children and in 2 Month-old Infants

Inclusion Criteria: * Male or female whose age on the day of randomization falls within one of the two age groups: 6 to less than (\<) 24 months (more than \[\>\] 6 months of age and not yet reached their 2nd year birthday), Cohorts 1 and 2 2 months (+/- 4 weeks), Cohorts 3, 4, and 5 * Cohorts 1 and 2 only: Subject is seronegative to both Respiratory Syncytial Virus (RSV) and human Parainfluenza Virus Type 3 (hPIV3) at Screening * Subject whose gestational age was greater than or equal to (\>=) 36 weeks * Subject is in general good health with normal growth (that is, body weight greater than (\>) third percentile per world health organization \[WHO\] simplified weight-per-age field tables * Subject's legal representative is available by telephone * Written informed consent and Health Insurance Portability and Accountability Act (HIPAA) authorization (if applicable) obtained from the subject's legal representative * Subject's legal representative is able to understand and comply with the requirements of the protocol as judged by the investigator * Subject is available to complete the follow-up period 1-year after receipt of the first dose of study vaccine * Subject's legal representative must be willing and able to bring the subject to the study site for evaluation of respiratory illness in accordance with the protocol. Exclusion Criteria: * Any fever (\>=100.4 degrees Fahrenheit \[\>=38.0 degrees Celsius\], regardless of route) or lower respiratory illness within 7 days prior to randomization * Moderate or severe nasal congestion that in the investigator's opinion could interfere with intranasal delivery of study vaccine * Acute illness (defined as the presence of moderate or severe signs and symptoms) at the time of randomization * Any drug therapy (chronic or other) within 7 days prior to randomization or expected receipt through the protocol-specified blood collection 28 days after each study vaccine dosing, except that infrequent use of over-the-counter medications for the systemic treatment of common childhood symptoms (that is, pain relievers, decongestants or cough suppressants) are permitted according to the judgment of the investigator * Any current or expected receipt of immunosuppressive agents including steroids (\>=2 milligram per kilogram \[mg/kg\] per day of prednisone or its equivalent, or \>=20 milligram per day \[mg/day\] if the subject weighs \>10 kilogram \[kg\], given daily or on alternate days for \>=14 days); children in this category should not receive study vaccine until immunosuppressive agents including corticosteroid therapy have been discontinued for \>=30 days; the use of topical steroids is permitted according to the judgment of the investigator * History of receipt of blood transfusion or expected receipt through the protocol-specified blood collection at 28 days after final study dosing * History of receipt of immunoglobulin products or expected receipt through the protocol-specified blood collection at 28 days after final study dosing * Receipt of any investigational drug within 60 days prior to randomization or expected receipt through 180 days after final study dosing * Receipt of any live virus vaccine (excluding oral polio vaccine and rotavirus vaccine) within 28 days prior to randomization or expected receipt within a 28-day window around any study vaccine dose * Receipt of any inactivated (that is, non-live) vaccine or oral polio vaccine or rotavirus vaccine within 14 days prior to randomization or expected receipt within a 14-day window around any study vaccine dose * Known or suspected immunodeficiency, including human immunodeficiency virus (HIV) infection * Expected to be living in the same home or enrolled in the same classroom at day care with infants \<6 months within 28 days after each dose * Living in a household with another child who is concurrently enrolled in a study of a live viral vaccine (including this study) * Expected contact with a pregnant caregiver within 28 days after each dose * A household contact who is immunocompromised; the subject should also avoid close contact with immunocompromised individuals for at least 28 days after any study vaccine dose * Expected household contact within 28 days after each dose with a health care provider for immunocompromised subjects or who is a day care provider for infants under the age of 6 months * History of allergic reaction to any component of the study vaccine * Previous medical history, or evidence, of an intercurrent or chronic illness that, in the opinion of the investigator, may compromise the safety of the subject * Known or suspected active or chronic hepatitis infection * History of medical diagnosis of asthma, reactive airway disease, wheezing requiring medication, cystic fibrosis, bronchopulmonary dysplasia, chronic pulmonary disease, medically confirmed apnea, hospitalization for respiratory illness or mechanical ventilation for respiratory illness (excludes elective mechanical ventilation during surgery for subjects in Cohorts 1 and 2) * Family member or household contact who is an employee of the research center or otherwise involved with the conduct of the study * Any condition that, in the opinion of the investigator, might interfere with study vaccine evaluation.